Question

Find the derivative of
y = sinx.cos X​

Answer 1

Answer:

cos^2 x - sin^2 x

Step-by-step explanation:

y = cosx(cos x) + (-sinx)sinx

y = cos^2 x - sin^2 x

Answer 2

Solution:-

Given :-

$\rm \implies \: y = \sin x. \cos x$

To find

$\rm \implies \: \dfrac{dy}{dx}$

Now we can write as

$\rm \implies \: \dfrac{d}{dx} \sin x .\cos x$

Using UV Method

$\rm \implies \: u \times \dfrac{dv}{dx} + v \times \dfrac{du}{dx}$

$\rm \implies \: \sin x \times \dfrac{d \cos x}{dx} + \cos x \times \dfrac{d \sin x}{dx}$

$\rm \implies \: \sin x \times - \sin x + \cos x \times \cos x$

$\rm \implies \: - \sin {}^{2} x + \cos ^{2} x$

$\rm \implies \cos ^{2} x - \sin ^{2} x$

Answer

the derivative of y = sinx.cosx is cos²x - sin²x