What is the d/(da)(1+6cos^2(a)+cos^4(a)) ?

The d/(da)(1+6cos^2(a)+cos^4(a)) is -4cos^3(a)sin(a)-6sin(2a)

What is the first d/(da)(1+6cos^2(a)+cos^4(a)) ?

The first d/(da)(1+6cos^2(a)+cos^4(a)) is -4cos^3(a)sin(a)-6sin(2a)

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\frac{d}{d a} (1 + 6 cos^{2} (a) + cos^{4} (a))

- 4 cos^{3} (a) sin (a) - 6 sin (2 a)

Solution steps

\frac{d}{d a} (1 + 6 cos^{2} (a) + cos^{4} (a))

Apply the Sum/Difference Rule:

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

= \frac{d}{d a} (1) + \frac{d}{d a} (6 cos^{2} (a)) + \frac{d}{d a} (cos^{4} (a))

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

\frac{d}{d a} (6 cos^{2} (a)) = - 12 cos (a) sin (a)

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

= 0 - 12 cos (a) sin (a) - 4 cos^{3} (a) sin (a)

Simplify

0 - 12 cos (a) sin (a) - 4 cos^{3} (a) sin (a) : - 4 cos^{3} (a) sin (a) - 6 sin (2 a)

= - 4 cos^{3} (a) sin (a) - 6 sin (2 a)

f (x) = x^{6} - x^{4} - 2

x (x^{2} + 4)^{0.5}

\frac{1}{( x - 5 ) ^{2}}

\frac{d}{d t} (12 + 6 t)

\frac{arctan ( x )}{2}

What is the d/(da)(1+6cos^2(a)+cos^4(a)) ?
The d/(da)(1+6cos^2(a)+cos^4(a)) is -4cos^3(a)sin(a)-6sin(2a)
What is the first d/(da)(1+6cos^2(a)+cos^4(a)) ?
The first d/(da)(1+6cos^2(a)+cos^4(a)) is -4cos^3(a)sin(a)-6sin(2a)