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Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation1 Mark
Question
Diffrentiate the following w. r. t. x.
$\cos ^3\left[\cos ^{-1}\left(x^3\right)\right]$
✓

Answer

Let $y=\cos ^3\left[\cos ^{-1}\left(x^3\right)\right]$
$=\left[\cos \left(\cos ^{-1} x^3\right)\right]^3$
$=\left(x^3\right)^3=x^9$
Differentiating w.r.t. x, we get
$\frac{d y}{d x}=\frac{d}{d x}\left( x ^9\right)=9 x ^8$

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