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

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

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

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

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

- 2 cos (2 x)

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - cos (2 x) \cdot 2

Simplify

= - 2 cos (2 x)

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