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Popular >

derivative of cos^3(x^2-x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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x \to 0 lim (\frac{x ^{2} - 8 x + 15}{5})

Frequently Asked Questions (FAQ)

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