A2) Find the derivative of the following functions: x² + 4 (a). f(x) x2 - 4 (b). f(x) = 2 tan-'(x) – 3" (c). f(x) = (x + 4 sin æ) (1 – 4 cos a) tanx (d). g(x) = 4 – secx

Q: 4. Find the derivative of the function f(x) = (sin x)c0s ". COS x

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Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

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Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: 2х- 3 3. У3 5x +1

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Q: Find the first derivative for y = 5 cos x

A: Given,          y=5cosx

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

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Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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Q: 10. Determine the derivative of the function with respect to x. y = sin?(x)

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Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

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Q: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Part 1 : Slope of tangent at (π2, π4) is given by dydx(π2, π4) ⇒y·sin 8x=x·cos 2x⇒ddx(y·sin…

Q: 1 14) Use the definition of derivative to find dx 3- х.

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Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: 3. Find the derivative y(15)of the function y = (x2 + x)sin(2x).

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Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: 2. Find the derivative of the function. y = e* In (sinæ)

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Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: Sin X I+ COS f' (x) =>

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Q: y = cof'/ x2-1 x²+

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Q: 4. Find the derivative of the functions. (2x2-3) a. y = (x247)5 sin x b. y = 1+cosx

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Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

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

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Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

A: we are given the function is  f(x)=1+sin2x2cos3x

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

Q: How do you solve question 10?

A: Given function is  By definition of derivative , we have

Q: 1. Find the first order derivative of u = x*.

A:

Q: 1) Find the derivative of the given function with respects to 0 y = 3lan In 3

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x

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Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 3x-4 1. Y= Arctan

A: To find second derivative of the given function.

Q: What is the derivative of the: y = (1 + cos2 x sin x2)3/2

A: Given: y=1+cos2x sinx232 differentiate with respect to x, dydx=ddx1+cos2x sinx232dydx=321+cos2x…

Q: c. Find the derivative of y =+- et x3 cOS X 2

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Q: 3. Find the derivative of the following function. 8(x) = cos"(vx)

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Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

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Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: B. Find the slope indicator (derivative) of the tangent lines of the given function and find the…

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Q: Q. 2. a) Find nth order derivative of f(x) = In(2x-7). b) Find 3rd order derivative of y with…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…