Question

the derivative of the function sin2xwith respect to x​

Answer 1

Answer:

$\boxed{\sf 2cos(2x)}$

Step-by-step explanation:

$\sf Possible \: derivation:$

$\sf \implies \frac{d(sin(2x))}{dx}$

$\sf Using \: the \: chain \: rule,$

$\sf \frac{d(sin(2x))}{dx} = \frac{dsin(u)}{du} \times \frac{du}{dx},$

$\sf where \: u = 2x \: and \: \frac{d(sin(u))}{du} = cos(u) :$

$\sf \implies cos(2x)( \frac{d(2x)}{dx} )$

$\sf Factor \: out \: constants:$

$\sf \implies 2cos(2x)( \frac{dx}{dx} )$

$\sf The \: derivative \: of \: x \: is \: 1:$

$\sf \implies 1 \times 2cos(2x)$

$\sf Simplify \: the \: expression:$

$\sf \implies 2cos(2x)$