What is the derivative of sin(4x-1/3 cos^2(4x)) ?

The derivative of sin(4x-1/3 cos^2(4x)) is 4cos(4x)+8/3 cos(4x)sin(4x)

What is the first derivative of sin(4x-1/3 cos^2(4x)) ?

The first derivative of sin(4x-1/3 cos^2(4x)) is 4cos(4x)+8/3 cos(4x)sin(4x)

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\frac{d}{d x} (sin (4 x) - \frac{1}{3} cos^{2} (4 x))

4 cos (4 x) + \frac{8}{3} cos (4 x) sin (4 x)

Solution steps

\frac{d}{d x} (sin (4 x) - \frac{1}{3} cos^{2} (4 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (4 x)) - \frac{d}{d x} (\frac{1}{3} cos^{2} (4 x))

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

\frac{d}{d x} (\frac{1}{3} cos^{2} (4 x)) = - \frac{8}{3} cos (4 x) sin (4 x)

= cos (4 x) \cdot 4 - (- \frac{8}{3} cos (4 x) sin (4 x))

Simplify

= 4 cos (4 x) + \frac{8}{3} cos (4 x) sin (4 x)

What is the derivative of sin(4x-1/3 cos^2(4x)) ?
The derivative of sin(4x-1/3 cos^2(4x)) is 4cos(4x)+8/3 cos(4x)sin(4x)
What is the first derivative of sin(4x-1/3 cos^2(4x)) ?
The first derivative of sin(4x-1/3 cos^2(4x)) is 4cos(4x)+8/3 cos(4x)sin(4x)