What is the derivative of sin^2(x^2-1) ?

The derivative of sin^2(x^2-1) is 4xsin(x^2-1)cos(x^2-1)

What is the first derivative of sin^2(x^2-1) ?

The first derivative of sin^2(x^2-1) is 4xsin(x^2-1)cos(x^2-1)

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derivative of

sin^{2} (x^{2} - 1)

4 x sin (x^{2} - 1) cos (x^{2} - 1)

Solution steps

\frac{d}{d x} (sin^{2} (x^{2} - 1))

Apply the chain rule:

2 sin (x^{2} - 1) \frac{d}{d x} (sin (x^{2} - 1))

= 2 sin (x^{2} - 1) \frac{d}{d x} (sin (x^{2} - 1))

\frac{d}{d x} (sin (x^{2} - 1)) = cos (x^{2} - 1) \cdot 2 x

= 2 sin (x^{2} - 1) cos (x^{2} - 1) \cdot 2 x

Simplify

= 4 x sin (x^{2} - 1) cos (x^{2} - 1)

What is the derivative of sin^2(x^2-1) ?
The derivative of sin^2(x^2-1) is 4xsin(x^2-1)cos(x^2-1)
What is the first derivative of sin^2(x^2-1) ?
The first derivative of sin^2(x^2-1) is 4xsin(x^2-1)cos(x^2-1)