What is the derivative of f(x)=sin^2(x^2) ?

The derivative of f(x)=sin^2(x^2) is 4xsin(x^2)cos(x^2)

What is the first derivative of f(x)=sin^2(x^2) ?

The first derivative of f(x)=sin^2(x^2) is 4xsin(x^2)cos(x^2)

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derivative of

f (x) = sin^{2} (x^{2})

4 x sin (x^{2}) cos (x^{2})

Solution steps

\frac{d}{d x} (sin^{2} (x^{2}))

Apply the chain rule:

2 sin (x^{2}) \frac{d}{d x} (sin (x^{2}))

= 2 sin (x^{2}) \frac{d}{d x} (sin (x^{2}))

\frac{d}{d x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

= 2 sin (x^{2}) cos (x^{2}) \cdot 2 x

Simplify

= 4 x sin (x^{2}) cos (x^{2})

What is the derivative of f(x)=sin^2(x^2) ?
The derivative of f(x)=sin^2(x^2) is 4xsin(x^2)cos(x^2)
What is the first derivative of f(x)=sin^2(x^2) ?
The first derivative of f(x)=sin^2(x^2) is 4xsin(x^2)cos(x^2)