What is the derivative of 2xsin(x+x^2cos(x)) ?

The derivative of 2xsin(x+x^2cos(x)) is 2sin(x)+4xcos(x)-x^2sin(x)

What is the first derivative of 2xsin(x+x^2cos(x)) ?

The first derivative of 2xsin(x+x^2cos(x)) is 2sin(x)+4xcos(x)-x^2sin(x)

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\frac{d}{d x} (2 x sin (x) + x^{2} cos (x))

2 sin (x) + 4 x cos (x) - x^{2} sin (x)

Solution steps

\frac{d}{d x} (2 x sin (x) + x^{2} cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x sin (x)) + \frac{d}{d x} (x^{2} cos (x))

\frac{d}{d x} (2 x sin (x)) = 2 (sin (x) + x cos (x))

\frac{d}{d x} (x^{2} cos (x)) = 2 x cos (x) - x^{2} sin (x)

= 2 (sin (x) + x cos (x)) + 2 x cos (x) - x^{2} sin (x)

Simplify

2 (sin (x) + x cos (x)) + 2 x cos (x) - x^{2} sin (x) : 2 sin (x) + 4 x cos (x) - x^{2} sin (x)

= 2 sin (x) + 4 x cos (x) - x^{2} sin (x)

What is the derivative of 2xsin(x+x^2cos(x)) ?
The derivative of 2xsin(x+x^2cos(x)) is 2sin(x)+4xcos(x)-x^2sin(x)
What is the first derivative of 2xsin(x+x^2cos(x)) ?
The first derivative of 2xsin(x+x^2cos(x)) is 2sin(x)+4xcos(x)-x^2sin(x)