Question

find dy/dx if y=sinx×cos2x​

Answer 1

Question:

$y = sinx \: cos</u><u>2</u><u>x$

Answer:

diff. w.r.t.x

$\frac{dy}{dx} = sinx \: cos</u><u>2</u><u>x \\ \\ \frac{dy}{dx} = sinx \frac{d \: \: }{dx} (cos</u><u>2</u><u>x)+ cos</u><u>2</u><u>x \frac{d}{dx} (sinx) \\ \\ \frac{dy}{dx} = sinx( - sin</u><u>2</u><u>x) </u><u>2</u><u>+ cos</u><u>2</u><u>x(cosx) </u><u>$

Formulae used:

$\star \: \frac{d}{dx} (x.y) = x \frac{d}{dx} (y) + y \frac{d}{dx} (x) \\ \\ \star \: \frac{d}{dx} sinx \: = cosx \\ \\ \star \: \frac{d}{dx} cosx = - sinx$

Answer 2

$\large \underline{ \red{ \boxed{ \bf \orange{Required \: Answer}}}}$