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Popular >

derivative of sin^2(x^2-1)

Solution

derivative of

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

Solution

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)

Popular Examples

integral of (e^{1/x})

\int (e^{\frac{1}{x}}) d x

integral of 1/(xsqrt(x^4-64))

\int \frac{1}{x x ^{4} - 64} d x

derivative of e^{2*(x-1})

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

integral of (-10x^2)/((x^3+2)^{-3)}

\int \frac{- 10 x ^{2}}{( x ^{3} + 2 ) ^{- 3}} d x

derivative of (250/((1+5x)^3))

\frac{d}{d x} (\frac{250}{( 1 + 5 x ) ^{3}})

Frequently Asked Questions (FAQ)

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)