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Popular Calculus >

derivative of sin^4(3x-4x^2)

Solution

derivative of

sin^{4} (3 x - 4 x^{2})

Solution

4 sin^{3} (3 x - 4 x^{2}) cos (3 x - 4 x^{2}) (3 - 8 x)

Solution steps

\frac{d}{d x} (sin^{4} (3 x - 4 x^{2}))

Apply the chain rule:

4 (sin (3 x - 4 x^{2}))^{3} \frac{d}{d x} (sin (3 x - 4 x^{2}))

= 4 (sin (3 x - 4 x^{2}))^{3} \frac{d}{d x} (sin (3 x - 4 x^{2}))

\frac{d}{d x} (sin (3 x - 4 x^{2})) = cos (3 x - 4 x^{2}) (3 - 8 x)

= 4 (sin (3 x - 4 x^{2}))^{3} cos (3 x - 4 x^{2}) (3 - 8 x)

Simplify

= 4 sin^{3} (3 x - 4 x^{2}) cos (3 x - 4 x^{2}) (3 - 8 x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sin^4(3x-4x^2) ?
The derivative of sin^4(3x-4x^2) is 4sin^3(3x-4x^2)cos(3x-4x^2)(3-8x)
What is the first derivative of sin^4(3x-4x^2) ?
The first derivative of sin^4(3x-4x^2) is 4sin^3(3x-4x^2)cos(3x-4x^2)(3-8x)