Question

Differentiate given problems w.r.t.x.

$si{n}^{3}x+co{s}^{6}x$.

Answer 1

Let y= $si{n}^{3}x+co{s}^{6}x$.

Differentiating w.r.t. x, we get

$\frac{dy}{dx}=\frac{d}{dx}$ $si{n}^{3}x+co{s}^{6}x$= $\frac{d}{dx}(sinx{)}^3+\frac{d}{dx}(sinx{)}^6$

= $3\left(sinx{)}^{3-1}\frac{d}{dx}\right(sinx)+6(cosx{)}^{6-1}\frac{d}{dx}\left(cosx\right)$

=$3si{n}^{2}cosx+6co{s}^{5}x(-sinx)=3si{n}^{2}xcosx-6sinxco{s}^{5}x$

= $3sinxcosx(sinx-2co{s}^{4}x)$