Differentiate the functions showing the general process in determining the derivatives. Using the delta y and x and applying limits .

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

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Q: Find the derivative of the function f(x) = 2sin x %3D

A: Given       f(x)=2sin x

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: Find the derivative. Simplify where possible. f(x) = tanh ( 1+ e2x  )

A: f(x) = tanh ( 1+ e2x  )

Q: Find the derivative. f(x) = tanh(x) f'(x) =

A: Using chain rule of differentiation

Q: Determine Step 3 using 4-Step Rule in finding the derivative of  y=2sin(x)cos(x).

A: Introduction: The four-step method to find derivatives is actually determining the derivative of a…

Q: find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A: Given that, y=(x3+cosx)-4

Q: . Find the equation of a line tangent to the graph of f (x) = cotx at x = T/4. .Find the derivative…

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Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: Compute the derivative using derivative rules.

A: Explanation Given that,  y=(kx+b)-13   Differentiate with respect to x both the sides…

Q: Find the derivative of the function.

A: We have a nested form of functions . We have to use chain rule of differentiation to find the…

Q: Find the derivative of the function: f(x) = ln X x+1* Is there a shortest way? Please explain.

A: We can find the answer in the following steps.

Q: calculate the derivative. y = sinh x tanh x

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Q: FInd the derivative using implicit differentiation rules x2+y2=x+y

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Q: find the derivative of y with respect to the appropriatevariable. y = sinh-1 √x

A: Find the derivative of y with respect to the appropriate variable.

Q: Find the derivative of the function f(x) = arctan ex

A: According to the question, we have to find the derivative of the function fx=arctan ex. The…

Q: What is the derivative of * y = arctan(x2 + 1)?

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Q: Find the derivative using the appropriate rule or combination of rules. y = x cos(1 − 3x)

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Q: calculate the derivative y = sech x coth x

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Q: find the derivative of y with respect to the appropriatevariable. = cosh-1 2√x + 1

A: Given: y=cosh-12x+1Here ,we havecoshy=2x+1Taking the derivatives on both…

Q: fcx)= Y文 メ ー^

A: Local extrema

Q: f (y) = 3secy tan y

A: Topic :- Derivative

Q: Find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A:

Q: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: Find the derivative of y(x) = (x+3) ¹/2 x+19 (Use symbolic notation and fractions where needed.) dx…

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Q: Find the Derivative of the hyperbolic function (3.11): y=sech(x)*(1+ln(sech x))

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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: find the derivative of y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: (a) h(x) = tan(r'sinx

A:

Q: Find the derivative of the function using chain rule. f(x) = esin?x

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Q: Find the derivative of the secant function y=secx.

A: The give function is y=secx.

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: Find the derivative. Simplify where possible. y = x tanh-lx + In /1 – x²

A: We have to find

Q: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: Find the derivative. Simplify where possible. f(x)  =tanh (1 + e2x)

A: Here given as fx=tanh1+e2x Since  ddxtanhx=sech2x

Q: Find the derivative of the function. f(x) = In(sinh(x)) %3D f '(x) = %3D

A:

Q: The first derivative of a continuous function y = f(x) is y' = x(x- 21). Find y" and then use the…

A: Given: i. The first derivative of a continuous function y=fx.ii. y'=xx-212 To Find: i. y''ii. Use…

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) f'(x) =

A: Given problem is :

Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: Find the derivative car (x+y) = yrinx

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Q: Find the derivative of the function y = tanh−1√x

A: To find the derivative of the given function.

Q: Find the derivative. f(x) = eX cosh(x) f'(x) =

A: First use relationship between hyperbolic function and exponential function convert coshx in…

Q: Find the derivative. f(x) = tanh(2 + e4x) f '(x)

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Q: Find the derivative of the function using the definition of derivative. g(t) = Vt %3D

A: Here, the given function is g(t)=5t. We need to find the derivative of the function g(t), using the…

Q: y=

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Q: Find the derivative. Simplify where possible. y = x tanh  -1 x +ln ( sqrt 1 - x 2 )

A: Given, y=xartanh⁡(x)+ln⁡(1−x2)can be rewritten asy=ln⁡(1−x2)2+xartanh⁡(x)