What is the derivative of f(x)=cos(x)+xsin(x) ?

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

What is the first derivative of f(x)=cos(x)+xsin(x) ?

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

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derivative of

f (x) = cos (x) + x sin (x)

x cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= x cos (x)

\frac{\partial}{\partial x} (4 x + 9 y)

\frac{\partial}{\partial x} (x^{4} + 5 x y^{9})

t \to 0 lim (t^{2})

\frac{\partial}{\partial y} (x ln (x + 2 y))

\frac{d}{d t} ((t + sin (t - 1))^{3} (t^{2} - 2)^{5})

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