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

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

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

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

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derivative of

f (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)

\int 9 sin^{3} (x) cos^{7} (x) d x

\int_{0}^{\infty} x d x

\frac{d}{d x} (a x e^{- 5 x})

\int 4 cot^{4} (x) d x

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