What is the derivative of-4cos(x+xsin(x)) ?

The derivative of-4cos(x+xsin(x)) is 5sin(x)+xcos(x)

What is the first derivative of-4cos(x+xsin(x)) ?

The first derivative of-4cos(x+xsin(x)) is 5sin(x)+xcos(x)

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

5 sin (x) + x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= 5 sin (x) + x cos (x)

What is the derivative of-4cos(x+xsin(x)) ?
The derivative of-4cos(x+xsin(x)) is 5sin(x)+xcos(x)
What is the first derivative of-4cos(x+xsin(x)) ?
The first derivative of-4cos(x+xsin(x)) is 5sin(x)+xcos(x)