What is the derivative of cos^{22}(x+1) ?

The derivative of cos^{22}(x+1) is -22cos^{21}(x)sin(x)

What is the first derivative of cos^{22}(x+1) ?

The first derivative of cos^{22}(x+1) is -22cos^{21}(x)sin(x)

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\frac{d}{d x} (cos^{22} (x) + 1)

- 22 cos^{21} (x) sin (x)

Solution steps

\frac{d}{d x} (cos^{22} (x) + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (cos^{22} (x)) + \frac{d}{d x} (1)

\frac{d}{d x} (cos^{22} (x)) = - 22 cos^{21} (x) sin (x)

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

= - 22 cos^{21} (x) sin (x) + 0

Simplify

= - 22 cos^{21} (x) sin (x)

What is the derivative of cos^{22}(x+1) ?
The derivative of cos^{22}(x+1) is -22cos^{21}(x)sin(x)
What is the first derivative of cos^{22}(x+1) ?
The first derivative of cos^{22}(x+1) is -22cos^{21}(x)sin(x)