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Derivative of Standard Functions

Question

Differentiate
$cos x$
$cos x$
${cos}^{2} x$
$- sin x$
$sin x$

A

{cos}^{2} x

B

sin x

C

cos x

D

- sin x

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Solution

Verified by Toppr

$y = cos x$
$\frac{d y}{d x} = lim h \to 0 \frac{f (x + h) - f (x)}{h}$
$= lim h \to 0 \frac{cos (x + h) - cos (x)}{h}$
$= lim h \to 0 \frac{- 2 sin (\frac{2 x + h}{2}) sin (h / 2)}{h}$
$= - sin x$
$∴ \frac{d y}{d x} = - sin x$

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