Find the equation of the tangent line to the curve at point (0, ln 2).   y=ln(e^x+e^4x)

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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Q: Compute the derivative of the function y=arcsin1√x at x=2.

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Q: Calculate the derivative with respect to x of the other variable appearing in the equation. exy =…

A: Given, exy=siny2

Q: Find the derivative of sinh(x)tanh(x).

A: As per our guidelines I am solving only first problem please repost other question.  y = sinh(x).…

Q: calculate the derivative. y = sinh(x2)

A: we have to find the derivative  y = sinh(x2)

Q: find the derivative of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

Q: find the equation of the tangent lines using implicit differentiation 2xy+x^2=3 at (-1,1) and…

A: Given: Equation of the curve,       To determine: Equation of the tangent line at (i) (-1, 1) (ii)…

Q: Use negative differential to obtain an equation of tangent curves at a given point.

A: Solve the following

Q: Find the second derivative and the points of inflection using the second derivative f(x) = ln(x) /…

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Q: Find the equilibria of the differential eq

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Q: .Find the derivative of the function y = cosh*x- sinh“ x

A: As per guidelines we can solve only one question at a time, if you need more answer kindly repost…

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: calculate the derivative. y = sinh(9x)

A: First of all, consider the formula for the chain rule and the given function y. Then assume u and v…

Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: Find the slope to the tangent line of the equation y2e2x = 3y+x² at (0,3) Hint: perform implicit…

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Q: calculate the derivative with respect to x. ln x + ln y = x − y

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Q: Find an equation of the tangent to the curve x+ Vy = 3 at point (4, 1). [Hint: Use implicit…

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Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

Q: Calculate the derivative. 1 y = log 5x y' =0

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Q: In(tanhx)

A: As we know that; The chain rule: fgx'=f'gx·g'x And ddxtanhx=sech2x Given: fx=lntanhx

Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Find dy/dx by implicit differentiation. x4 + yA 5

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Q: Find the derivative of the function y = arctan x+ 1+x?

A: To find: The derivative of the function . Calculation: Find the derivative of the function.

Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x)

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Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

Q: Compute the derivative. Use logarithmic differentiation where appropriate. 10 1+ dx 10 1+ dx 10 In…

A: Answer: ddx1+10xx = ln1+10x-10x+10 1+10xx

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

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Q: Va2-x² Y=Arc sin + a

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Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

Q: wwww To find the slope of the tangent line to y = ln(x²) at the point (1,0) we must find the…

A: Recall: Slope of the tangent line

Q: Find the derivative. Simplify where possible. |(a) y = ln(coshx)

A: Find the derivatives

Q: Find the equation of the tangent line to the curve y = ln(4 ln x) at the point where x = e. %3D

A: It can be solved using differentiation.

Q: Find the equation of the tangent line to the curve given by f(x) = x2 ln x at the point  (1, 0)

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (sec (ln θ))

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Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: Find the values of x in the interval [0,2π] where the tangent line to the graph of y= sinxcosx is…

A: Given:y=sinxcosx,     [0,2π]

Q: calculate the derivative y = tanh−1(ln t)

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Q: Find the derivative of y with respect to x.   y= tan-1 *square root (16x2-1) +csc-1*4x ,   x greater…

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Q: calculate the derivative y = sinh(ln x)

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Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: 2. Calculate the derivative of y = arccos(e arcsin(x2)

A: Let u=arcacos(e^x) and v=arcsin(x^2), then y=u/v

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: Find the derivative of s(*) - L Int dt 1+t

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Q: Solve the first and second derivative of y = cosh2x+ sinhx

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Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

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