Question

If y = (sin x²)²,  then `("d"y)/("d"x)` is equal to ______.

Options

• 4x sin 2x² 

• –x cos x²

• 2x sin 2x² 

• –x sin 2x²

Answer 1

If y = (sin x²)²,  then `("d"y)/("d"x)` is equal to 2x sin 2x² .

Explanation:

y = (sin x²)² 

∴ `("d"y)/("d"x) = 2  sin x^2 * "d"/("d"x) (sin x^2)`

= `2  sin x^2 * (cos x^2)* "d"/("d"x) (x^2)`

= `2  sin x^2 * (cos x^2) * 2x`

= `2x (2 sin x^2 cos x^2)`

= `2x sin 2x^2`