Question

Find derivative of $2^x$

Answer 1

Let $y=2^x⟹\log y=\log 2^x$

$⟹\log y=x\log 2$

Now differentiating:

$⟹\frac{1}{y}\frac{dy}{dx}=\frac{dx}{dx}\log 2+x\frac{\log 2}{dx}$

$⟹\frac{1}{y}\frac{dy}{dx}=\log 2+0$

$⟹\frac{dy}{dx}=y\times \log 2$

$⟹\frac{dy}{dx}=2^x\log 2$