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If
, find 
$y=\cos 3x$ Let $u=3x$ and $y=\cos u$ $\dfrac{du}{dx}=3$ and $\dfrac{dy}{du}=-\sin u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 3\times -\sin u$ $\dfrac{dy}{dx}= -3\sin u$ $\dfrac{dy}{dx}= -3\sin 3x$ $\dfrac{d^{2}y}{dx^{2}}= 3\times -3\cos 3x$ $\dfrac{d^{2}y}{dx^{2}}= -9Read more
and 
and 
See lessLet
If
, find 
$y=\cos 3x$ Let $u=3x$ and $y=\cos u$ $\dfrac{du}{dx}=3$ and $\dfrac{dy}{du}=-\sin u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 3\times -\sin u$ $\dfrac{dy}{dx}= -3\sin u$ $\dfrac{dy}{dx}= -3\sin 3x$
and 
and 
See lessLet
If
, find 
$y=3\cos 2x$ Let $u=2x$ and $y=3\cos u$ $\dfrac{du}{dx}=2$ and $\dfrac{dy}{du}=-3\sin u$ $\dfrac{dy}{dx}= \dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}= 2\times -3\sin u$ $\dfrac{dy}{dx}= -6\sin u$ $\dfrac{dy}{dx}= -6\sin 2x$
and 
and 
See lessLet
If
, find 
$y=3\cos x+3\sin x-\cos 2x$ $\Rightarrow \dfrac{dy}{dx}=-3\sin x+3\cos x+2\sin 2x$
See lessIf
, find 
$y=3\cos x+3\sin x-\cos 2x$ $\Rightarrow \dfrac{dy}{dx}=-3\sin x+3\cos x+2\sin 2x$ $\Rightarrow \dfrac{d^{2}y}{dx^{2}}=-3\cos x-3\sin x+4\cos 2x$
See lessIf
, find 
$y=\tan 2x$ Let $u=2x$ and $y=\tan u$ $\Rightarrow \dfrac{du}{dx}=2$ and $\dfrac{dy}{du}=\sec^{2}x$ $\Rightarrow \dfrac{dy}{dx}=\dfrac{du}{dx}\times \dfrac{dy}{du}$ $\Rightarrow \dfrac{dy}{dx}=2\times \sec^{2}x$ $\Rightarrow \dfrac{dy}{dx}=2\sec^{2}x$
and 
and 
See lessLet
Using quotient rule, find
if 
Let $u=\sin x$ and $v=1+\cos x$ $\Rightarrow \dfrac{du}{dx}=\cos x$ and $\dfrac{dv}{dx}=-\sin x$ $\Rightarrow \dfrac{dy}{dx}=\dfrac{v\dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^{2}}$ $\Rightarrow \dfrac{dy}{dx}=\dfrac{(1+\cos x)^{2}\times \cos x-\sin x\times -\sin x}{(1+\cos x)^{2}}$ $\Rightarrow \dfrac{dy}{dRead more
Let
and 
from trig. identities
See lessFind
if 
$y=x^{2}\cos 2x$ Let $u=x^{2}$ and $v=\cos 2x$ $\Rightarrow \dfrac{du}{dx}=2x$ and $\dfrac{dv}{dx}=-2\sin 2x$ $\Rightarrow \dfrac{dy}{dx}=v\dfrac{du}{dx}+u\dfrac{dv}{dx}$ $\Rightarrow \dfrac{dy}{dx}=\cos 2x\times 2x+x^{2}\times -2\sin 2x$ $\Rightarrow \dfrac{dy}{dx}=2x\cos 2x-2x^{2}\sin 2x$ $\RightaRead more
and 
and 
See lessLet
Find
if 
$y=3\cos x-\sin x$ $\Rightarrow \dfrac{dy}{dx}=-3\sin x-\cos x$
See lessIf
, find 
$y=x^{3}-3x^{2}+6x-1$ $\Rightarrow \dfrac{dy}{dx}=3\times x^{3-1}-2\times 3x^{2-1}+6$ $\Rightarrow \dfrac{dy}{dx}=3x^{2}-6x+6$
See less