What is the derivative of cos^2(x-sin^2(x)) ?

The derivative of cos^2(x-sin^2(x)) is -sin(2x)*2

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

The first derivative of cos^2(x-sin^2(x)) is -sin(2x)*2

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

- sin (2 x) \cdot 2

Solution steps

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

Simplify

cos^{2} (x) - sin^{2} (x) : cos (2 x)

= \frac{d}{d x} (cos (2 x))

Apply the chain rule:

- sin (2 x) \frac{d}{d x} (2 x)

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

\frac{d}{d x} (2 x) = 2

= - sin (2 x) \cdot 2

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