Question

Take the derivative of each of the following 3t = 1. g(x) = (3x2 – 22 )4 2. r(t) t2+1 3. f(z) = (5x+1)3 sin^2 4. f(x) = cos (ex?)

Answer 1

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Here is the attached Image of explanation of each question.

Solution for Question 1

4 Given g(x) = (3x2 – 2x) let y = 3x2 2x g(x) =yt Now; gf(x) = 44() g'(x) = d[yA] . dy dy g'(x) = 4y3. dy dx dac dx We have dy dac y= 3x2 - 2x = 3 d (12) - 0(2) de dx dy 3(2x) 2² ena da put dy in ean lis, we have da 27 ena g'(x) g'(x) = 4y3 [ 6x 4 (68_2* enz). (32e²_2²)3

Solution for Question 2

r(t) = 3+ +2 +1 3t d [***] P = WW dt = (@P vodu u-dv at dt v2 Hence, (*) = (1+27) P 7€ - (72) (i+z+) It 자 2 z (H 27) r(A) (72) 7E 3(+2+2) (Z²+1)2 3 (1 – t2) (1+ t²2 r' (t)

Solution for Question 3

f (x) - (5x+1)? sinta u f'(x) = d [5x+1} (sinta] dx = (5x + 4(sin x ) + Sinºx 4( 5x+1)3 dre dac de dac = (5x+33.d (sinte).d (sinx) + sintxe. d (584+13.d(52+1) dsinn) d(54+1) = (5x+3)? + sinise.cose + sint ac 3(5x+1)? 5 = f'() = 4 sine.coste ( 5x+3)3 + Is sints. (5*+1) 2

Solution for Question 4

- cos (62) f(c) f'(X) d coscevezy dae =d[ces ce)) dcery.d(x2) dez) dx d(x2) 2 e = - sinlezzy ex2 f(x) - 2 a qoe ede? sin(ex2)

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