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Popular >

derivative of sin^3(x^2-1)

Solution

\frac{d}{d x} (sin^{3} (x^{2} - 1))

Solution

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

Solution steps

\frac{d}{d x} (sin^{3} (x^{2} - 1))

Apply the chain rule:

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

= 3 (sin (x^{2} - 1))^{2} \frac{d}{d x} (sin (x^{2} - 1))

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

= 3 (sin (x^{2} - 1))^{2} cos (x^{2} - 1) \cdot 2 x

Simplify

= 6 x sin^{2} (x^{2} - 1) cos (x^{2} - 1)

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\int \frac{x + arctan ( x )}{1 + x ^{2}} d x

derivative of x^{arcsin(x})

\frac{d}{d x} (x^{a r c s i n (x)})

derivative of (4x+4sqrt(1+x)/(x^2-1))

\frac{d}{d x} (\frac{4 x + 4 1 + x}{x ^{2} - 1})

integral of (8x^2+10)/(x^3+5x)

\int \frac{8 x ^{2} + 10}{x ^{3} + 5 x} d x

x^3=(2sqrt(y^5+4))/(5y^4y^')

x^{3} = \frac{2 y ^{5} + 4}{5 y ^{4} y ^{^{'}}}

Frequently Asked Questions (FAQ)

What is the derivative of sin^3(x^2-1) ?
The derivative of sin^3(x^2-1) is 6xsin^2(x^2-1)cos(x^2-1)
What is the first derivative of sin^3(x^2-1) ?
The first derivative of sin^3(x^2-1) is 6xsin^2(x^2-1)cos(x^2-1)