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Popular >

derivative of cos^7(2x^2+1)

Solution

\frac{d}{d x} (cos^{7} (2 x^{2} + 1))

Solution

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

Solution steps

\frac{d}{d x} (cos^{7} (2 x^{2} + 1))

Apply the chain rule:

7 (cos (2 x^{2} + 1))^{6} \frac{d}{d x} (cos (2 x^{2} + 1))

= 7 (cos (2 x^{2} + 1))^{6} \frac{d}{d x} (cos (2 x^{2} + 1))

\frac{d}{d x} (cos (2 x^{2} + 1)) = - sin (2 x^{2} + 1) \cdot 4 x

= 7 (cos (2 x^{2} + 1))^{6} (- sin (2 x^{2} + 1) \cdot 4 x)

Simplify

= - 28 x cos^{6} (2 x^{2} + 1) sin (2 x^{2} + 1)

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Frequently Asked Questions (FAQ)

What is the derivative of cos^7(2x^2+1) ?
The derivative of cos^7(2x^2+1) is -28xcos^6(2x^2+1)sin(2x^2+1)
What is the first derivative of cos^7(2x^2+1) ?
The first derivative of cos^7(2x^2+1) is -28xcos^6(2x^2+1)sin(2x^2+1)