Mathematicsddxsin3sin-1x

$\frac{d}{d x} (\sin (3 \sin^{- 1} x))$

A
3x-4x³
B
4x³-3x
C
12x²-3
D
3-12x²

Solution:

The given function is

$\begin{array}{rcl} y & = & \sin (3 \sin^{- 1} x) \\ = & \sin (\sin^{- 1} (4 x^{3} - 3 x)) \\ = & 4 x^{3} - 3 x \end{array}$

differentiatie both sides

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d}{d x} (4 x^{3} - 3 x) \\ = & 12 x^{2} - 3 \end{array}$

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