What is the derivative of x*sin(x+cos(x)) ?

The derivative of x*sin(x+cos(x)) is xcos(x)

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

The first derivative of x*sin(x+cos(x)) is xcos(x)

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

x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= x cos (x)

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