Find the derivative of the function using the definition of derivative. ft) = 3.5t2 + 2t %3D f'(t) ) = State the domain of the function. (Enter your answer using interval notation.)

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: Can you help me with this problem step by step?

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Q: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

A:

Q: Find the derivative of the function. 5x g(x) = [¨ cos(r}]dt cosx

A: We will use Lebnitz rule to differentiate the function .

Q: Find the derivative of the function. y = cos(aª + x*) y'(x) =

A: f(x)  =  cos x4 + a4ddx f(x) = f'(x) =…

Q: Find the derivative of the function y = etan(e) y' =

A: Explanation of the answer is as follows

Q: Find the derivative of the function. x coS X y = e*cos x

A: Differentiation is the rate of change of some variable with respect to the other variable. Chain…

Q: Can you help me with this problem step by step?

A: Consider the given equation:

Q: Find the derivative of the function.

A:

Q: Find the derivative of the function y = ex(sin x + cos x)

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Q: Find the derivative of the function. y = sin ( xcosx )

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Q: Eョ2 T -(X子 ノ = (X)J fi(3)

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Q: Find the derivative of the function below. F(x) = arctan e a*) f'(x) =

A:

Q: Find the derivative of the function. F(x) = et dt

A: The function is given as F(x)=∫xx2et4 dt. The Leibnitz rule of differentiation under the integral…

Q: Find the derivative of y with respect to x. y=secant-1 (x 2+1),   x greater than 0.   dy/dx=????

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Q: Find the derivative of the function.

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Q: find the derivative of y with respect to the givenindependent variable. y = xπ

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Q: Calculate the derivative.

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Q: Determine the derivative of y=| 3e2x with respect to x ((x+1) (Inex² O Integrato the fo IL

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Q: Find the derivative of the function. y = sin-(cos-(t))

A: Given: y=sin-1cos-1t To determine: The derivative of the given function.

Q: What is the derivative of y = ekx? For what values of k does this rule apply?

A: Given function is, y=ekx. The derivative of the given function is found as follows: dydx=ddxekx=kekx

Q: Find the derivative of y with respect to the independent variable. y = 3 cOS TTO

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. Inx y = x7

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Q: Find the derivative of the function. f(z) = V - VE f '(x) =

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Q: Find the derivative of y with respect to x. y= csc^-1 (x^2+1) , x>0

A: Given ,

Q: Compute the derivatives. Use the fact that e2+x = e2 . ex to find d/dx (ex+2).

A: ddxex+2

Q: Ө+5 y = Өcos 0

A:

Q: B) Using the definition of derivative, find dy -if y = dx 1-x

A:

Q: y=In(x dy -

A: Given : y = ln1xx-5

Q: Find the derivative of the function.

A:

Q: Evaluate the derivative of the function y = 2tan ",²+In (e +e).

A:

Q: Find the derivative of the function. y = tanh-(6x) V6 1+ 6x y' =

A: derivative of the function..

Q: Find the derivative of hyperbolic function 1) h(x) = sinh(r2)

A: we have to find derivative

Q: Find the derivative of the function. y = cos(a + x*) У (x) %3

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Q: Find the derivative of the given function. dx %3D

A:

Q: Find the derivative of the function. 1 y = 4/x +3x dy dx |00 %3D

A: Use formulas of derivatives to find dy/dx

Q: Find the derivative of the (e) h(x) = e5 sin (Væ) + a° sec ()-

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the derivative of the given function. t q= tan Vi+2 dq dt

A: The following formulas of differentiation can be used to solve the given derivative. i d dttan…

Q: Compute the high-accuracy central difference approximation for the first derivative of the function…

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Q: Find the given flx), + 2x derivative of function. %3D a+x

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Q: Find the derivative of the function. F(x) = et dt F'(x) = %3D

A: We know that by Leibniz rule of differentiation under integral sign, we have

Q: Find the derivative of g(x) = fecost dt.

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Q: The first derivative of the given function is y = sec?. %3D 2х + 1

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Q: Find the derivative of y with respect to t. y = 5sin (4t)

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Q: Find the derivative of y with respect to x. y = sec -1 (2x? + 1), x>0 ..... dx

A: The derivative of y with respect to x is to be calculated, where y=sec-12x2+1, x>0. The results…

Q: Find the derivative.

A: Given,

Q: Find the derivative of the function. F(x) etd dt F'(x) =

A:

Q: Find the derivative of y with respect to the given independent variable. e* cos' x (1) y= x+1

A:

Q: Find the derivative of y = f(x) = x cos(x).

A: y =f(x) = x cos xf'(x)=ddx (x cos x)

Q: Find the first derivative of the function below: f(#) = cosh(cot(z² – 2x – 7)) %3D

A: