Question

If y = sin x², then dy/ dx using chain rule is​

Answer 1

Answer :

Derivative of (sin x)² = Sin2x

Solution :

‌Using chain rule :

‌Let y = sinx²

$‌\sf \dfrac{d}{dx}sin^2 x \times \dfrac{d}{dx}sinx$

‌We know that,

$‌\sf \: Derivative \: of \:\boxed{\sf \color{red} x^n = n.x^{n-1}}$

$‌\sf \: Derivative \: of \:\boxed{\sf \color{red} sin x = cos x}$

‌Applying this here, we got :

‌$\sf 2sin^{2-1} \times cos x \\ \\ \implies\sf 2sin x cos x$

we know that,

$\red\bigstar\boxed{\sf 2sinxcox=Sin2x}$

So,

$\implies\sf \underline{\boxed{\bf\pink{ \sin 2x}}}$

Hence,

Derivative of (sinx)² or sin²x is sin2x .

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More to know :

• $\sf\dfrac{d}{dy}tan x = sec^2 x$

• $\sf\dfrac{d}{dy}cosec x = -cosec x.cotx$

• $\sf\dfrac{d}{dy}sec x = tan x.sec x$

• $\sf\dfrac{d}{dy}cot x = -cosec^2 x$

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