Question

Find the derivative of sin inverse of
$(3x - 4x$
​

Answer 1

$\Large\color{lime}{\textsf{\textbf{ \:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\;Question:-}}}$

$\large\rm$

find derivative of sin-¹ (3x-4x)

$\large\rm$

$\Large\red{\textsf{\textbf{ \:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\;Answer:}}}$

$\large\rm$

$\large\tt{\:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\; \dfrac{d}{dx} \: sin^{-1} ( 3x-4x)}$

$\large\rm$

$\large\tt{ \:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\;= \dfrac{d}{dx} \: - \: sin^{-1} x}$

$\large\rm$

$\large\tt{\:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\; = - \left( \dfrac{d}{dx} \: sin^{-1} x \right)}$

$\large\rm$

use chain rule

$\large\rm$

$\large\tt{ \:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\; = - \dfrac{\frac{d}{dx} x}{\sqrt{1-x^2}}}$

$\large\rm$

$\large\tt{ \:\:\:\;\:\;\;\;\;\;\;\:\;\;\;\;\;\;\; = - \dfrac{1}{\sqrt{1-x^2}}}$

$\large\rm$

Additional Information:-

$\large\rm$

Domain $\large\tt = \{ x \in \mathbb{R} | -1 \leqslant x \leqslant 1\}$

Range $\large\tt =\Bigg \{ y \in \mathbb{R} \Bigg | \dfrac{-\pi}{2} \leqslant y \leqslant \dfrac{\pi}{2} \Bigg \}$