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Differentiation of Derivatives — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsDifferentiation of Derivatives2 Marks
Question
Differentiate $\sin ^2\left(x^2\right)$ w.r.t. $x^2$.
✓

Answer

Let $x^2=t$
So,
$
\begin{aligned}
\frac{d\left[\sin ^2(x)^2\right]}{d x^2} & =\frac{d\left(\sin ^2 t\right)}{d t} \\
& =2 \sin t \times(\sin t)^{\prime} \\
& =2 \sin t \times \cos t \\
& =2 \sin \left(x^2\right) \cos \left(x^2\right)
\end{aligned}
$

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