6) Find the derivative of the following functions 6.1) a(x) = x²(sin x)(cot x)e" 6.2) b(x) = ()-4

Q: Differentiate the following. (a) y = sin(x3) (b) y = sin3(x)

A: For (a), y'=sin x3'     By the chain rule,   =cosx3x3'     =cosx3· 3x2

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

A: Given

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: 10. Find the 87th derivative of y = cos(2x) at IT

A:

Q: (1) Using the definition of derivative, find the derivative of th following functions: (a) y = xvx²…

A:

Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: 5. Calculate the derivative of the following functions. DO NOT SIMPLIFY a. f(x) = x³ (arctan(x²) –…

A:

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

A:

Q: Is it possible to evaluate the anti-derivative below? | (x + 1) cOS (2x) cos (x2) dx

A:

Q: Find the derivative of the following function. f(x)=ln(e2x+3) evaluated at X=ln 4 The value of…

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Q: +0.0001) – 1, tan(4 4. Which derivative is approximated by 0.0001

A:

Q: 01:- Find the first order derivative of each of the following functions: (1+x)3 sec(x2) y = ex.sin2…

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Q: What is the derivative of x sin(x) at the point (6,5)? 2 O 1 O-1 O None of the above

A:

Q: 4. Find the derivative of the following function. 1+ sin x 8(x) = 1+ cos x

A:

Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

A:

Q: e. f. f(x) = cot(-) X f(x) = sin(x³ - x)

A:

Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

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: 4.) f (x) 3D х2 – 1

A:

Q: 1-cos 4x Find the derivative of y sin 4x

A:

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

A: Given

Q: 4. Find the derivative of the following function. 1+ sinx g(x) = - V1+ cos x

A: Given: gx=1+sinx1+cosx for finding derivative of given function, first we simplify given expression…

Q: f (x) = 1

A:

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

A:

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

A: Given,

Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

A:

Q: Find the derivative of the following. y = x2 sin x + 2x cos x - sin x

A: We need to find the derivative of the following, y=x2sinx+2xcosx-sinx

Q: 7. Consider the function f(x) X - 3 a. Using the definition of the derivative at a point, calculate…

A: Given : f(x) = x / x - 3   (1) f' (2)  (2) tangent line when x = 2 (3) normal line when x = 2

Q: 3 Find the derivative of the following functions. (Answer five only) 1-r = 120-1 - 40-3 +0-4 2- y…

A:

Q: 1. Find the derivative the following functions y=-10x+ cosx y=x'sinx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 7. y = cos(sin(In(æ))

A:

Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

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Q: Find the derivative of y with respect to s. (56° +3) У3 sec

A:

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: f(x) = sin (x³)

A:

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: Find the derivatives of the functions defined as follows.

A: Given, y=-cos2x+cosπ6

Q: Q1/ Choose the appropriate function for this derivative sin x cos x V1+ cosx 2/1+ cos x

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Q: 5. Find the derivative of --( 1 + sin 0 cos 0

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Q: 5. Find the derivative of h(x) = cos(sin(cosx)).

A:

Q: (x² +SJ° In 14-X つ. dr

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: 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: 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: 1+sin 2x 1) Find the derivative of f(x) = 2 cos x

A: To find The derivative of given f(x)

Q: 3 Find the derivative of the following functions. (Answer five only) 1-r= 120--4e-3+e- 2- y = (sin x…

A: differentiate

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: y = k2 (Arc sin) – xvk2 – x² where k is a constant.

A: