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Find
for 
$y=3x^{3}$ $\dfrac{dy}{dx}= 3\times 3x^{3-1}$ $\dfrac{dy}{dx}= 9x^{2}$ $\dfrac{d^{2}y}{dx^{2}}= 2\times 9x^{2-1}$ $\dfrac{d^{2}y}{dx^{2}}= 18x$
See lessFind
for 
$y=3x^{3}$ $\dfrac{dy}{dx}= 3\times 3x^{3-1}$ $\dfrac{dy}{dx}= 9x^{2}$
See lessIf
, find 
$y=\dfrac{x^{3}-2x+1}{x^{2}}$ $y=x-\dfrac{2}{x}+\dfrac{1}{x^{2}}$ $y=x-2x^{-1}+x^{-2}$ $\dfrac{dy}{dx}= 1-(-1)\times -2x^{-1-1}+(-2)\times x^{-2-1}$ $\dfrac{dy}{dx}= 1-2x^{-2}-2x^{-3}$ $\dfrac{dy}{dx}= 1-\dfrac{2}{x^{2}}-\dfrac{2}{x^{3}}$
See lessDifferentiate
wrt x
$y=\sin 3x$ Let $u=3x$ and $y=\sin u$ $\dfrac{du}{dx}=3$ and $\dfrac{dy}{du}=\cos u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 3\times \cos u$ $\dfrac{dy}{dx}= 3\cos u$ $\dfrac{dy}{dx}= 3\cos 3x$
and 
and 
See lessLet
Differentiate
wrt x
$y=\sin (2x-4)$ Let $u=2x-4$ and $y=\sin u$ $\dfrac{du}{dx}=2$ and $\dfrac{dy}{du}=\cos u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 2\times \cos u$ $\dfrac{dy}{dx}= 2\cos u$ $\dfrac{dy}{dx}= 2\cos (2x-4)$
and 
and 
See lessLet
Differentiate
wrt x
$y=\cos (2x+5)$ Let $u=2x+5$ and $y=\cos u$ $\dfrac{du}{dx}=2$ and $\dfrac{dy}{du}=-\sin u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 2\times -\sin u$ $\dfrac{dy}{dx}= -2\sin u$ $\dfrac{dy}{dx}= -2\sin (2x+5)$
and 
and 
See lessLet
Differentiate
wrt x
$y=\cos 6x$ Let $u=6x$ and $y=\cos u$ $\dfrac{du}{dx}=6$ and $\dfrac{dy}{du}=-\sin u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 6\times -\sin u$ $\dfrac{dy}{dx}= -6\sin u$ $\dfrac{dy}{dx}= -6\sin 6x$
and 
and 
See lessLet
Differentiate
wrt x
$y=\sin 4x$ Let $u=4x$ and $y=\sin u$ $\dfrac{du}{dx}=4$ and $\dfrac{dy}{du}=\cos u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 4\times \cos u$ $\dfrac{dy}{dx}= 4\cos u$ $\dfrac{dy}{dx}= 4\cos 4x$
and 
and 
See lessLet
Differentiate
wrt x
$y=\tan 2x$ Let $u=2x$ and $y=\tan u$ $\dfrac{du}{dx}=2$ and $\dfrac{dy}{du}=\sec^{2}u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 2\times \sec^{2}u$ $\dfrac{dy}{dx}= 2\sec^{2}u$ $\dfrac{dy}{dx}= 2\sec^{2}2x$
and 
and 
See lessLet
If
, find 
$s=\sin 3t$ Let $u=3t$ and $s=\sin u$ $\dfrac{du}{dt}=3$ and $\dfrac{ds}{du}=\cos u$ $\dfrac{ds}{dt}= \dfrac{du}{dt}\times \dfrac{ds}{du}$ $\dfrac{ds}{dt}= 3\times \cos u$ $\dfrac{ds}{dt}= 3\cos u$ $\dfrac{ds}{dt}= 3\cos 3t$
and 
and 
See lessLet