9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x - 1)³dx = (a) 5 (b) 4 (c) -e²-cos1+c (c) 2 (d) e* – sin r+c (d) o

Q: Find the derivative of f(x) =tan-1 (cos 6x) 6 sin 6x a. f'(x) = 1+cos? 6x - sin 6x b. f'(x) = 1+cos?…

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Q: (a) [ dx ? 元+1

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Q: [CLO-2] Find the derivative of 5 cosx f (x) = 4 sinx+3 O 21 – 6 cosx O ( 7 cosx+2)2 6 – 10 cosx (3…

A: Given:         fx=5cosx4sinx+3   Differentiating on both sides       f'x=ddx5cosx4sinx+3 Taking…

Q: Find the second derivative of the function y=x(x² – 1)² A) None of the given choices B) 2x(5x2 - 6)…

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Q: Find the third derivatives of the function f (x) = e sin (2x)

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Q: 5. Find the derivative of the function. f(x) = x°/1- 8x x(16-136x) 2/1-Sr x'(16+136x) f (x)3D 2/1-8x…

A: The function is given by,

Q: Given f"(x) = 2x? – 4x3- 7x +3, f'(1) = -6, and f(1) = -7. %3D Find f'(x) and f(x). Part 1: Find the…

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Q: 3. Evaluate the derivatives of the following: i. 2t +3 ii. x' sin x iii. In(3x-4) iv. (2x +5)"

A: i. Quotient Rule:  The Quotient Rule for differentiation is given by, Evaluate the derivative of…

Q: Derive the formula dy/dx= 1/ (1 + x2) for the derivative of y = tan-1 x by differentiating both…

A: Given,

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A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS.

A: Hey! Done below. Please ask for further clarifications:)Explanation:1.)     f(x)=cos2x=>…

Q: 2+ cosh r (r² + 4) Compute the derivative of y = In I - (r+ 1) Compute the derivative of f(x) =…

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Q: DERIVATIVE

A: We have to find the third derivative of  given function

Q: O Find the derivative of the following functions: L 2+3 (a). f(z) = 2-3 (b). f(z) = 2 tan (z) – 7…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use the rule for recipocals : f '(x) f?(x) d 1 dx [ f(x) to find the following derivatives…

A: Given: Reciprocal Rule: ddx1f(x)=−f'(x)f2(x) Find: 1)  ddx1x2+2x+1=?2)  ddx1sinx+ex=?3)  ddxπx+1=?

Q: Suppose that f(4) = 2 and f' (4) = h(x) = (2x² + 3in (f(x)))² h' (4) = (b) h(x) = 20f(x) e-2x + 3…

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Q: Step 2: Step 3: Sten 4:

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Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

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Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…

A: Given:- y = (-7x2-5x+5) (sin(x) +11x)  To find:- Derivative of y

Q: 2. Computing Derivatives; Compute each derivative using the derivative rules: d (a) (cos-(1+ 2*) +…

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Q: Q-7: [3+2 marks] a) Find an approximate value for x (to 2 decimal places) if 5 = 3 In x - b) Find y"…

A: Dear student since the policy is to answer first one only, kindly repost the other.

Q: What is the derivative of f(z) = (z³ –- (z – 1)º)*? %3D

A: Given function is f(x) = (x3 - (x-1)3)3