What is the derivative of f(x)=a^5+cos^5(x) ?

The derivative of f(x)=a^5+cos^5(x) is -5cos^4(x)sin(x)

What is the first derivative of f(x)=a^5+cos^5(x) ?

The first derivative of f(x)=a^5+cos^5(x) is -5cos^4(x)sin(x)

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derivative of

f (x) = a^{5} + cos^{5} (x)

- 5 cos^{4} (x) sin (x)

Solution steps

\frac{d}{d x} (a^{5} + cos^{5} (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a^{5}) + \frac{d}{d x} (cos^{5} (x))

\frac{d}{d x} (a^{5}) = 0

\frac{d}{d x} (cos^{5} (x)) = - 5 cos^{4} (x) sin (x)

= 0 - 5 cos^{4} (x) sin (x)

Simplify

= - 5 cos^{4} (x) sin (x)

What is the derivative of f(x)=a^5+cos^5(x) ?
The derivative of f(x)=a^5+cos^5(x) is -5cos^4(x)sin(x)
What is the first derivative of f(x)=a^5+cos^5(x) ?
The first derivative of f(x)=a^5+cos^5(x) is -5cos^4(x)sin(x)