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

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

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

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

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

- sin (x) + sin (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - sin (x) - (- sin (2 x))

Simplify

= - sin (x) + sin (2 x)

y = - cot (x)

y = (\frac{2}{3})^{x}

f (z) = 2 z^{2}

f (x) = - x^{2} + 5 x

y = 3 x^{5}

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