Differentiate: h(x) = ... cot x -e h'(x) = csc2 x ... A e" (cot a + csc? x) cot² x ... h'(x) =' e" (csc? x – cot x) ... © h'(x) csc² x -e" cot x (csc x – 1) ... D cot? x = (x),4

Q: 1. Dx[arcsin(2x + 1)]

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Q: IX. Find y' if 1. (5 pts.) y = 2 In (cos (Tx)) 2. (6 pts.) y = csc² (Arcsec (Va) + e-)

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Q: x*(1 + 2x') dx

A: This is the problem of definite integral with substitution. ∫01x21+2x35dx Substitute 1+2x3=t6x2dx=dt…

Q: S sec*x csc*x dx

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Q: nx ( X

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Q: 12. Given: f(x)dx = 4 S(»)dx = -1. and Find: (a)

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Q: Suppose that a 6-foot tall person is 12 feet away from an18-foot tall lampost. (a) use similar…

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Q: |tan' x.sec x.dr = tan x +C %3D

A: This question is based on indefinite integral.

Q: Differentiate. V = 3 - sec(x) tan(x)

A: The given function y is in the quotient form. Apply the quotient rule formula

Q: y = csc (x’ + 10x), Find dy/dx O (7x6 + 10) csc (x7 + 10x) cot (x7 + 10x)

A: Given: y=cscx7+10x

Q: Scot"(2) cot³ (x) dx

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Q: Find y". y = 5 cot X

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Q: Scot³ x ( cz) ¹4 dx sec x tan x 5.

A: Follow the procedure given below.

Q: cosy = x, so implicit differentiation gives - sin(y)y' = 1, or

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Q: If u=e*? then du= ... %3D dx 2xe* dx 2x 2xe*

A: The chain rule states that ddxfgx=f'gxg'x.

Q: x³ +4x² + x – 1 dx 2 X 16. .3 2 1 x' + x'

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Q: Differentiate y = (tanx-1) /secx

A: we need to evaluate derivative of y = tan x - 1sec xthis can be done by using quotient rule. That…

Q: Differentiate f(r)= tan(3x). Use exact values. f'(x) = %3D

A: Given ,f(x)=tan-1(3x)We know that, ddx(tan-1(x))=1x2+1Differentiate w.r.t. xApply chain…

Q: y" +y- tanx An 8.

A: Given