x sin(-) +x for x +0 Decide if the function, f (x) = , is differentiable at x = 0. Try zooming in on a graphing calculator, 0 for x= or calculating the derivative f' (0) from the definition.

Q: y = sec? x tan x

A: Consider the given function: Here the objective is to find the derivative of a given function.

Q: Find the derivative. Simplify where possible. y  = x Sinh-1 (x /3)  - √ (9+x2)

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Q: Find the derivative of the function. Simplify where possible. – tan""(x – /1 + x² ) %3D

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Q: Find the derivative. Simplify where possible. y  = Sinh-1(tan x)

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Q: Find the derivative of the function y = cot^-1 x^2– cos^-1 (x + 1/x – 2). %3D

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Q: Find the derivative of function and simply it whenever possible y= ln(ln sec x)

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: f(θ) = 4 sin(θ) - θDifferentiating, we get  f'(θ) = 4 cos(θ) - 1 f'(0) = 4 cos(0) - 1 = 4 - 1 = 3y -…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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Q: Find the derivative of the function. Simplify where possible. 60. y = arctan I+x

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Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

Q: Find the derivative. Simplify where possible.  f(x)= ex cosh x

A: Given function is

Q: Find the derivative using logarithmic differentiation if sin^-1 (2x). y = (tan x) where 0 < x < 1/2…

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Q: Find the derivative of the function. Simplify where possible: y=tan^-1(x-sqrt(1+x^2))

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Q: Find the derivative. Simplify where possible.

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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: Find the derivative. Simplify where possible. f(x) =ln  ( cosh x )

A: fx=lncoshx

Q: ■ Find the derivative of the function. Simplify wherepossible.  y = arctan sqrt ( (1-x)/(1+x))

A: Given function is y=arctan1-x1+x We know that ddxarctanx=11+x2 Therefore, dydx=11+1-x1+x2ddx1-x1+x

Q: Find the derivative of y = tan 3x

A: Given function is: y = tan 3x We have to find the derivative of y with respect to x.

Q: Use the h --> 0 definition of the derivative for each function f and value x=c for  f(x)= sin x,  x…

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Q: tan-'(nx) e IT X

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Q: Find the derivative of y = sin 2

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Q: Find the 40th derivative of the function f(x) = cos(x). The answer is function

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Q: Find the indicated derivative. f (x) = x° sin x; find f(4)(x).

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of…

A: The slope of tangent to a curve y=fx  at point a,b is given by dydxx=a.

Q: Find the derivative. Simplify where possible. f(x) = x sinh  x - cosh x

A: The given function is fx=xsinhx-coshx.

Q: 25

A: Given function is x2+y22=254xy2 We have, some rule of differentiation, ddxxn=nxn-1 ddxuv=vddxu+uddxv…

Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

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Q: Find the derivative of the function. f(x) = ln(2 − x2)   Thank you for your help!

A: Given function f(x) = ln(2-x2). Here we need to find the derivative of f(x) with respect to x.We use…

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: 3. Give the definition of a derivative of a function f of one variable at a point xo. /2 Find the…

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Q: Find the derivative of y = cot^-2(x)

A: Derivative of Apply chain rule to take derivative

Q: Find the derivative of the function. Simplify where possible. y   =arctan(cos θ)

A: Given:y=arc tancosθFormula:ddxtan-1u=11+u2.dudx

Q: Find the derivative of the function. Simplify where possible. y   = Cos-1(Sin-1t)

A: y=cos-1sin-1t

Q: Find the derivative of the following function. X- y = 3 sin x -3 dx X- sin x =

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Q: The derivative of y=sin^{5}x

A: Differentiate using the chain rule dy/dx= dy/du * du/dx

Q: Find the derivative. f(x) = 2^x {ln[cot(x)]}^2

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Q: Find the derivative. Simplify where possible. y =coth  - 1 ( sec x)

A: We have to differentiate the function: y=coth-1sec x We know the formula of differentiation,…

Q: Find the derivative of the function, using the differentiation rules developed in this chapter.…

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Q: Find the derivative of the function y = sin^-1 x/sqrt 1 + x^2 – tan^-1 x. %3D

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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 31th derivative of the function f(x) = cos(x). The answer is function

A: f(x)=cos(x) f'(x)=-sin(x) f"(x)=-cos(x) f"'(x)=sin(x)

Q: Find the derivative of the function. Simplify where possible.

A: Here given function gx=1-x2 cos-1x

Q: Solve for derivative. y = (x + cos x) ( 1 - sin x)

A: Given          y = (x + cos x) ( 1 - sin x)

Q: Find the derivative of f(x) = 3/x at x = 3 by using the definition of derivative. Note that you will…

A: Given,f(x) = 3x at x = 3

Q: Find the derivative of the function. Simplify where possible: 32) y=tan^-1(x-(sqrt(1+x^2)))

A: some important Derivatives :   1. ddxtan-1x = 11+x22. ddxxn = n*xn-13. ddxx = 12x4.ddxconstant = 0

Q: Find the derivative of the function. y = 2 tan-(sin x) y' =

A: Using derivat formulas.

Q: Find the derivative. Simplify where possible. g(x) =   cosh (   ln x )

A: Given: gx=coshlnx

Q: Find the derivative of the function. simplify where possible: 30) y=(x*cos^-1(x))-(sqrt(1-x^2))

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Q: 3 sin(x) +x² In(x) – 2x Find the derivative of f(x) = using derivative rules.

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