Question

If $y=\cos \left(3{\cos }^{-1}x\right)$, then $\frac{d^{3}y}{d{x}^3}$=

• A. $0$
• B. $12$
• C. $24$
• D. $24x$

Answer 1

The correct option is C $24$

$y=\cos \left(3{\cos }^{-1}x\right)$

$y=\cos \theta$ be $3{\cos }^{-1}x=\theta$

${\cos }^{-1}x=\frac{\theta }{3};(x=\cos \frac{\theta }{3})$

$\cos \theta =\cos 3\frac{\theta }{3}$

$=4{\cos }^3\frac{\theta }{3}-3\cos \frac{\theta }{3}$

$y=4x^3-3x$

${}^1=4\times 3x^2-3$

$y^{1}1=12\times 2x-0$

$y^{111}=12\times 2\times 2$

$\therefore \frac{d^{3}y}{d{x}^3}=24$ option $C$