. Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using h=0.2,h=0.02 and h=0.4 determine bounds for the approximation errors.

Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: Find the first derivative of the following functions with respect to x: a) y= Inx3 b) y = ln (÷) c)…

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Q: Find the derivative of ywith respect to x in the following functions: 18x y (ans.: (3x-2 a) y= and…

A: Derivative of uv uv' = u'v-v'uv2

Q: Compute the first and second derivatives of (x+4)e^x. Give the intervals wherethe function isa)…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Find the derivative of the following function. y (In ]x + 4|)7 dy

A: Differentiate w.r.t to x

Q: Which of the following is the derivative of * f (x) = In(tanhæ)?

A: Given function is : fx=lntanhx To find the derivative of fx tanhx is written astanhx=ex-e-xex+e-x

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A: We will do all three parts.

Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

A: The three point end point formula with error is where h is the step size. If the step size is…

Q: Find the derivative with rea If f00=(13x-26X +26)e nederivative with respeet X 1 =C13x-26X+26)e

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Q: What is the approximate derivative of f(x) = x²ex, using backward-difference approach at x=2 and a…

A: The formula for the backward difference is f'x=fxi+1-fxih Now, h=0.1xi=2xi+1=xi+h=2+0.1=2.1fx=x2ex

Q: Compute the derivatives of the following functions. 4 y = Vx + cot(x5) x²e2x3 f (x) In(x4+2)

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Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

Q: 2. Compute the second derivative, f"(x), of the function f(x) = e*. %3D

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Q: Find the actual error when the first derivative of f (x) = e-2x at x = 1 is approximated by the…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: 17. a. s = ln(4x) Inz I b. 1 IN C. IN d. 1 4x

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Q: Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

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Q: Compute forward difference approximations for the first derivative of the function, y =[ eln(x)2, at…

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Q: Verify that the derivative and integral results for a general base b reduce to the expected results…

A: Note that ddxbux=lnbeuxu'x,∫bxdx=bxlnb+C.

Q: Evaluate the derivative of mq4.4.png cosh (bVx3 f(x) = a ln sinh(cx2) if a = 69, b = 0.6, and c = 6…

A: Given function: fx=alncoshbx3sinhcx2 To find: The derivative of the function f'(7) using…

Q: Evaluate the derivative of e22.1.png acos(b/x) f(x) = x2 if a = 73 and b = 0.7 at x = 5 using FDA…

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Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

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Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

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Q: Evaluate the derivative of indicated order of the following functions: d2 (x cos(x² + 3x) а. dx2 d…

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Q: Q2 find the derivative of the following: 1) y = 2sin?(5x) ,2) y = lnx'ncosh 5x ,3) xsin-14y = y…

A: See the attachment

Q: Find the actual error when the first derivative of f (x) = e-2* at x = 1 is approximated by the…

A: It is known that ddxekx=kex. The actual error is calculated by subtracting the true value from the…

Q: If you use the two-point central difference formula with h=0.1 to approximate the derivative of…

A: Given: fx=1x , x=2, and h=0.1 To find: Approximate the derivative using the two-point central…

Q: Birinci mertebeden geri yön sayısai Ay O a) y': h Vy O B) y'= O NS) Vy y'= h

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Q: Estimate the true percent relative error for the first derivative of the function, y = e*cos(x?), at…

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Q: Find the derivative of the following functions without skipping steps w = tan (y) + cos (3z) -…

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Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

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Q: Verify that each of the following difference approximations for the first derivative provides the…

A: As each approximation has independent of previous one . So according to guideline , I am verifying…

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: Compute the derivative of h(sin(x)) at x = T/6, assuming h'(0.5) = 10:

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Q: Use backward, forward , and centered difference approximation to estimate the second derivative of…

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Q: Evaluate the second derivative of e22.1.png ... acos(byx) f(x) x2 if a = 165 and b = 0.3 at x = 3…

A: Follow step 2nd and 3rd.

Q: Apply the first order forward difference formula to find the derivative at x = 2.1. fx) 1.2 0.694444…

A: We need to find the derivative of the function f(x) at x=2.1 by applying first order forward…

Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) = x2 if a = 149 and b = 0.3 at x = 3…

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Q: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

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Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: Find the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

A: Solution

Q: Evaluate the second derivative of h z f8.png asin (bvx3) f(x) c2x + In(kx) if a = 16.55, b = 3, c =…

A: The Backward Difference Approximation(BDA) uses the formula below to approximate the double…

Q: Use the forward-difference formula to approximate the derivative of f(x) = In(x) at ¤o = 1.8 using…

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Q: Use the forward-difference formula to approximate the derivative of f(x) = In(x) at ro 1.8 using…

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Q: The derivative of y with respect to given a = 1 is Onone of the choices O y = yx³-1 O V = 0 = = 9 *…

A: I have stated the used formula in the solution

Q: Find the second derivative of y with respect to x if y = x In(x) - X. А.X In(x) B. In(x) C. In(x)/x…

A: The given function is y=x ln(x)-x

Q: Use backward, forward , and centered difference approximation to estimate the second derivative of…

A: The formulas for the backward, forward, and central differences to approximate the second derivative…

Q: Evaluate the derivative of Z F5.png sin (b V) x² f(x) = acosh %3D cx3 if a = 12.91, b = 3, and c = 6…

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Q: Find the actual error when the first derivative of f(x) = e* at x = 1 is approximated by the…

A: Find the exact value of derivative of f(x) at x=1 and approximate value of derivative  of f(x) from…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: