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

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

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

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

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

2 sin (2 x)

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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)

Simplify

= 2 sin (2 x)

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