Question

differentiate cosesc ²(5x²+3x-5)³ with respect to x​

Answer 1

$\boxed{\underline{\textsf{Formulas :}}}$

1. $\frac{d}{dx}$(cosecx) = - cosecx cotx

2. $\frac{d}{dx}(x^{n})=n\:x^{n-1}$

$\boxed{\underline{\textsf{Solution :}}}$

Now, $\frac{d}{dx}${cosesc²(5x²+3x-5)³}

= $\frac{d}{dx}${cosec(5x²+3x-5)³}²

= 2 cosec(5x²+3x-5)³
{- cosec(5x²+3x-5)³
cot(5x²+3x-5)³}
$\frac{d}{dx}$(5x²+3x-5)³

= - 2 cosesc²(5x²+3x-5)³
cot(5x²+3x-5)³ * 3(5x²+3x+5)²
$\frac{d}{dx}$(5x²+3x-5)

= - 6 cosesc²(5x²+3x-5)³
cot(5x²+3x-5)³(5x²+3x-5)²
(10x+3)