What is the derivative of 4sin(x+4xcos(x)) ?

The derivative of 4sin(x+4xcos(x)) is 8cos(x)-4xsin(x)

What is the first derivative of 4sin(x+4xcos(x)) ?

The first derivative of 4sin(x+4xcos(x)) is 8cos(x)-4xsin(x)

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\frac{d}{d x} (4 sin (x) + 4 x cos (x))

8 cos (x) - 4 x sin (x)

Solution steps

\frac{d}{d x} (4 sin (x) + 4 x cos (x))

Apply the Sum/Difference Rule:

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

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

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

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

= 4 cos (x) + 4 (cos (x) - x sin (x))

Simplify

4 cos (x) + 4 (cos (x) - x sin (x)) : 8 cos (x) - 4 x sin (x)

= 8 cos (x) - 4 x sin (x)

What is the derivative of 4sin(x+4xcos(x)) ?
The derivative of 4sin(x+4xcos(x)) is 8cos(x)-4xsin(x)
What is the first derivative of 4sin(x+4xcos(x)) ?
The first derivative of 4sin(x+4xcos(x)) is 8cos(x)-4xsin(x)