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

The derivative of sin(x+xcos(x)) is 2cos(x)-xsin(x)

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

The first derivative of sin(x+xcos(x)) is 2cos(x)-xsin(x)

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

2 cos (x) - x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= 2 cos (x) - x sin (x)

What is the derivative of sin(x+xcos(x)) ?
The derivative of sin(x+xcos(x)) is 2cos(x)-xsin(x)
What is the first derivative of sin(x+xcos(x)) ?
The first derivative of sin(x+xcos(x)) is 2cos(x)-xsin(x)