* find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the direetion of miximum decrease of Ş at the Point P

Q: Find y(0.2) for y"=xz²-y², xo=0,yo-1,20-0, with step length 0.2 using Runge-Kutta 2 method (2nd…

A: To find- Find y0.2 for y'' = xz2 - y2, x0 = 0, y0 = 1, z0 = 0, with step length 0.2 using…

Q: Find partial derivative, zg and Zy for the following function: e 2x²+3y Z =

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Q: dw y of w=- dt H.W: Use the chain rule to find the derivative 1 with x= cos t, y= sin² t, z =- dw…

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Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

Q: find the directions in which the functions increase and decrease most rapidly at P0 . Then find the…

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Q: Find aw/@s and @w/at using the appropriate Chain Rule. Function Values w = y3-10x2y X = e, y = e S =…

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Q: Q2: Use the Chain Rule to find the indicated point partial derivative. U = x² + yz, x = prcose, y =…

A: Differential calculus

Q: Find the firs t derivative of the f anction y=4sin[sselur)] at the Point x= T

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Q: Find indicated nh order partial derivative: ap+qu 2. if u= (x – xo)P(y- yo)ª %3D

A: We will find the required partial derivative as following.

Q: 9. Find the constants a, b and c of cubic function f (x) = ax³ + bx + c such that : • The slope of…

A: Given that, f(x) = ax3 + bx  + c Slop of tangent line at x = 3 is 0. f'(1) = 24 f(x) croses the x…

Q: Q6/(A)Evalute y ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: find the partial derivative of the function with respectto each variable. P(n, R, T, V ) = nRT/V…

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Q: COE Compute the mixed second order partial derivative of z =

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Q: Q2: Use the Chain Rule to find the indicated point partial derivative. U = x² + yz, x = prcose,y =…

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Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: Find the length of the curve y =x2/8 − ln(x) on the interval [1, 2].

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Q: Q3: Find the first derivative of y= cos(x) at x= t/2 using a step size of h= Tt/12. Use forward and…

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Q: Q2. Find the second order partial derivative of F(x.y) = x³+ x°y°- 2y² w.r.t. x at (2,1).

A: Given:        Fx,y=x3+x2y3-2y2  taking first partial derivative with respect to x.…

Q: Q4/ Find the value of the following partial derivative (choose O 1- If w(x, y) = Ln(ey+/5xy)),find…

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Q: 5) y>10 (3v-1) (1+5w)

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Q: Can you help me step by step?

A: To determine the value of first and second derivative of the function

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: Q. No. 5. Find the Derivative of the Given fur a) y= ev1n x( Inx) +2x b) f(x) = %3D a+x

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: We must now find the slope of the tangent line at the point of tangency, (1, In 2), by aun buneinɔ…

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Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: 10x Find the directional derivative of f(x,y) = at P(5,0) in the x + y direction of Q(4, –3). NOTE:…

A: Here is the solution:

Q: Q1: Find partial derivatives of the function with respect with each variable 4) f(x, y) = Vx² + y²…

A: We find the partial derivatives of the given function f(x, y)=x2+y2, by using the definition of…

Q: O Find the value dz at the point (4,-1,-3) dz if 2. lnx -x +4 = 0 + y. function of he two…

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Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: Q2) Find the derivative of the function at Po in the direction of A. g(x, y) = x – (y²/x) + V3 sec-'…

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Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: 1) Find the Linearization x of the function -V1+2x when x is near 0 Find the equation of the tangent…

A: As per Bartleby guideline if more than one question is asked only first question to be answered…

Q: dz Find the value of at the point (1,1,1) if the equation 6xy +z°x-2yz = 5 defines z as a function…

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Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: U = x² + yz, x = prcos0,y = prsin0,z = p +r au aU and au Find when p = 2,r = 3,0 = 0 дө - dp' ar

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Q: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

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Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: (c) Use the chain rule to find the derivative of the function z = 2r*y³ – ry² along the curve given…

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Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y)=-3xy + 5y², P₁(-10,2),…

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Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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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: