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Find the value of
if 
and 
$a=\log_{2}3$ and $b=\log_{8}3$ $a=\log_{2}3=\log 3\div \log 2$ $b=\log_{3}8=\log 8\div \log 3$ $ab=\dfrac{\log 3}{\log 2}\times \dfrac{\log 8}{\log 3}$ $ab=\dfrac{\log 8}{\log 2}$ $ab=\dfrac{\log 2^{3}}{\log 2}$ $ab=\dfrac{3\log 2}{\log 2}=3$
and 
See lessFind the derivative of
$y=2x^{2}+3$ $\dfrac{dy}{dx}=2\times 2x^{2-1}+0$ $\dfrac{dy}{dx}=4x^{1}$ $\dfrac{dy}{dx}=4x$
See lessFind the derivative of
$y=2x^{2}-5$ $\dfrac{dy}{dx}=2\times 2x^{2-1}-0$ $\dfrac{dy}{dx}=4x^{1}$ $\dfrac{dy}{dx}=4x$
See lessFind the derivative of
$y=x^{2}-x+1$ $\dfrac{dy}{dx}=2\times x^{2-1}-1\times x^{1-1}+0$ $\dfrac{dy}{dx}=2x^{1}-x^{0}$ $\dfrac{dy}{dx}=2x-1$
See lessIf angle
is 
, evaluate 
$\cos 135^{0}$ $135$ can be found in the second quadrant and cosine is negative there $\cos 135^{0}=-\cos (180^{0}-135^{0})$ $\Rightarrow -\cos 45^{0}=-\frac{\sqrt{2}}{2}=0.7071$
can be found in the second quadrant and cosine is negative there
See lessGiven
, find 
$s=2t^{2}-3t$ $\dfrac{ds}{dt}=2\times 2t^{2-1}-1\times 3t^{1-1}$ $\dfrac{ds}{dt}=4t^{1}-3t^{0}$ $\dfrac{ds}{dt}=4t-3$
See lessGiven
, find 
$y=3x^{2}+x-1$ $\dfrac{dy}{dx}=2\times 3x^{2-1}+1\times x^{1-1}-0$ $\dfrac{dy}{dx}=6x^{1}+x^{0}$ $\dfrac{dy}{dx}=6x+1$
See lessDifferentiate with respect to
: 
$y=(2x-1)^{2}$ Let $u=2x-1$ and $y=u^{2}$ $\dfrac{du}{dx}=2$ and $\dfrac{dy}{du}=2u$ $\dfrac{dy}{dx}=\dfrac{du}{dx}\times \dfrac{dy}{du}$ $\dfrac{dy}{dx}=2\times 2u$ $\dfrac{dy}{dx}=4u$ $\dfrac{dy}{dx}=4(2x-1)=8x-4$
and 
and 
See lessLet
Find
if 
$y=4x^{-2}$ $\dfrac{dy}{dx}=-2\times 4x^{-2-1}$ $\dfrac{dy}{dx}=-8x^{-3}$ $\dfrac{dy}{dx}=-\dfrac{8}{x^{3}}$
See lessFind the derivative of
$y=3-x^{2}$ $\dfrac{dy}{dx}=0-2\times x^{2-1}$ $\dfrac{dy}{dx}=0+x^{0}-2x^{1}$ $\dfrac{dy}{dx}=1-2x$
See less