Question

please answer the question
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Answer 1

Please refer to image

basic steps

use formula to differentiate a function in division

which states

if

$f = \frac{x - y}{z}$

then

differentiation

= [{(dy/dx of x) X y} - {(dy/dx of y) X x}] / z^2

Answer 2

Answer:

$Y = \frac{x {}^{5} - cos x }{sinx}$

Using quotient rule,

$\frac{dy}{dx} = \frac{VU {}^{1} - UV {}^{1} }{V {}^{2} }$

Differnatatiating with respect to X

Now,

$\frac{dy}{dx} = \frac{sinx. \frac{d(x {}^{5} - cosx) }{dx} - ({x}^{5} - cosx). \frac{ d(sinx)}{dx} }{(sinx) {}^{2} }$

$\frac{dy}{dx} = \frac{sinx.(5x {}^{4} - ( - sinx) - ( {x}^{5} - cosx).( cosx)}{(sinx) {}^{2} }$

$\frac{dy}{dx} = \frac{sinx.(5x {}^{4} + sinx) - cosx.(x {}^{5} - cosx) } { {(sinx)}^{2} }$

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