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

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

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

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

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derivative of

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