What is the derivative of f(x) g(x) in terms of f and g? Compute the derivative of -sin(x) · 2x=1 (simplification not necessary)

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

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Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: 1/x using the definition o

A: we have to find the derivative of f(x) using the first principal. f(x)=x+1x

Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin(x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: Find the derivative of 1 f(x) || 1+ Vx using the definition of derivative. State the domain of the…

A: We have to find the derivative of the given function by using the definition of derivative.

Q: Find fi( using the derivative rules tanx y2-3

A: Given, the function is                         We have to find the derivative of this function i.e.…

Q: 1. Find the derivative of f(x) = tan³(sinx) + %3D

A: The given function isf(x)=tan3(sinx)+x3+3x4

Q: Find the derivative of f(x) = tan(sin(2x))

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Q: 2. Use rules of differentiation to find the derivative of the function 5a° (x- +3) g(x) = x2 +1 Show…

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Q: Find the derivatives of the function f(x) from the first principle  sin2x

A: Answer and explanation is given below...

Q: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

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Q: 8. Find the derivative of f(x) = (1+x³)' ( 14x + - ) using differentiation rules.

A: topic - derivative of a function

Q: Find the second derivative of the function.

A: Given: fx=x cosx Now to find the derivative of the given function, Differentiate given function with…

Q: compute the derivative.  f (x) = (cos2 x)cos x

A: To compute the derivative.  f (x) = (cos2 x)cos x

Q: Find the derivative of the function. f(x) = sin-(4x) f'(x) = %3D

A: The given function is: f(x)=sin-1(4x) To find f'(x) here.

Q: Find the derivative f(x) = [sin(4* + x)][cos(x* + 4) %3D

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Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: Calculate the derivative of f(x) = x^(1/ln(x)). What can be said about f(x) based on its derivative…

A: Consider the function,

Q: Find the derivative of the function using the definition of derivative. f(x) = x4 f'(x) = %3D

A: To find the derivative of the given function using the definition of derivative.

Q: Find the 73rd derivative of the function f(x) = 2 sin(x). f (73) (x)

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Q: Compute the derivative of the function y = 8 sin-(x) at the point x = (Use symbolic notation and…

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Q: What is the derivative of f(x) = tan-(x)? %3D

A: We can solve this as follows:

Q: Find the derivative of f(x) = tan (cosx) ++

A: Important Derivatives:1. ddxxn = nxn-12. ddx tanx = sec2x3. ddx cosx = -sinx

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

A: Using chain rule of differentiation.

Q: 2. Determine the derivative of f(x) = sin-'(2x)

A: Topic = Derivative

Q: How do you find the derivative of f(x)= sec(x)tan(x)?

A: Some properties of derivatives:Following are some of general derivatives and derivatives of…

Q: Find the derivative of the function cos (x) using the definition

A: We have to find the derivative of cos (x) by using definition of derivative

Q: Find the derivative of f (x) = sin (5x) %3D

A: The given function is f(x)=sin3(5x)                     differentiate with respect to x,

Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

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Q: Derive the formula for the derivative with respect to x of sec x.

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Q: Find the derivative of the function by using thẻ Product Rule. Simplify your answer. f(x) = (Vx -…

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Q: Find derivative of the f(x) = sin-1*- 1 x+1 function

A: To find the derivative of the function

Q: Find the derivative of f(x)=x2-3x. Use the result to find the slope of the tangent line to the curve…

A: Given: fx=x2-3x To Find: The derivative of the given function and the slope of the tangent line at…

Q: How do you prove the general power rule of derivatives using the inverse property (x^n=e^(nlnx))?

A: The general power rule:

Q: 2. Evaluate derivative of the following function applying rules of differentiation: 7- 2x S(x) (Зх —…

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Q: f(x) = x' tan (5x)

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

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

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Q: What is the derivative of f(x) sec(tanx)?

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

A: Here given function gx=1-x2 cos-1x

Q: Find the derivative of f(x) = (-x3 - 2x² - 2x) sin (x). Do not include "f'(x) =" in your answer.…

A: The given function is: fx=-x3-2x2-2xsinx   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: What is the derivative of f(x) = (tan^-1)((3+x)/(1-3x))

A: Given:f(x)=(x+3)arctan(x)1-3xf'(x)=ddx(x+3)arctan(x)1-3x=ddx(x+3)arctan(x)·(1-3x)-(x+3)arctan(x)·ddx…

Q: Find the derivative of  f(x) = tan(cos(x^2))

A: f'(x) = d (tan(cos x2)dx  f'(x) = sec2(cos(x2))d cos x2dx               because   d (tan(x))dx =…

Q: What is the derivative of f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-1

Q: Find the derivative of the trigonometric function: f (x) -3 cos x + x* sin x

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Q: State the notation/symbol for: derivative of y with respect to x derivative of f(x) second…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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

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Q: 1. 1. f(x) = 4x³ · cos x

A: Given: fx=4x3.cosx

Q: 4 Find the derivative of f(x) using first principle %3D 3x2-3 of differentiation.

A: