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Mathematical Methods — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsMathematical Methods2 Marks
Question
Find the derivatives of the functions.
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Answer

Using, $\frac{d}{d x}\left[f_l(x) \times f_2(x)\right]=f_1(x) \frac{d f_2(x)}{d x}+\frac{d f_1(x)}{d x} f_2(x)$
For $f_1(x)=x^3$ and $f_2(x)=\sin x$
$ \frac{d}{d x}\left(x^3 \sin x\right)= x^3 \frac{d(\sin x)}{d x}+\frac{d\left(x^3\right)}{d x} \sin x$
$= x^3 \cos x+3 x^2 \sin x \ldots\left[\because \frac{d(\sin x)}{d x}=\cos x\right]$

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