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Popular >

d/(da)(cos^4(a)+sin^4(a))

Solution

\frac{d}{d a} (cos^{4} (a) + sin^{4} (a))

Solution

- 4 cos (a) sin (a) cos (2 a)

Solution steps

\frac{d}{d a} (cos^{4} (a) + sin^{4} (a))

Apply the Sum/Difference Rule:

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

= \frac{d}{d a} (cos^{4} (a)) + \frac{d}{d a} (sin^{4} (a))

\frac{d}{d a} (cos^{4} (a)) = - 4 cos^{3} (a) sin (a)

\frac{d}{d a} (sin^{4} (a)) = 4 sin^{3} (a) cos (a)

= - 4 cos^{3} (a) sin (a) + 4 sin^{3} (a) cos (a)

Simplify

- 4 cos^{3} (a) sin (a) + 4 sin^{3} (a) cos (a) : - 4 cos (a) sin (a) cos (2 a)

= - 4 cos (a) sin (a) cos (2 a)

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Frequently Asked Questions (FAQ)

What is the d/(da)(cos^4(a)+sin^4(a)) ?
The d/(da)(cos^4(a)+sin^4(a)) is -4cos(a)sin(a)cos(2a)
What is the first d/(da)(cos^4(a)+sin^4(a)) ?
The first d/(da)(cos^4(a)+sin^4(a)) is -4cos(a)sin(a)cos(2a)