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

The derivative of-x^2sin(x)+4xcos(x)+2sin(x) is -x^2cos(x)-6xsin(x)+6cos(x)

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

The first derivative of-x^2sin(x)+4xcos(x)+2sin(x) is -x^2cos(x)-6xsin(x)+6cos(x)

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derivative of

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

- x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (4 x cos (x)) = 4 (cos (x) - x sin (x))

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

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

Simplify

- (2 x sin (x) + cos (x) x^{2}) + 4 (cos (x) - x sin (x)) + 2 cos (x) : - x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

= - x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

What is the derivative of-x^2sin(x)+4xcos(x)+2sin(x) ?
The derivative of-x^2sin(x)+4xcos(x)+2sin(x) is -x^2cos(x)-6xsin(x)+6cos(x)
What is the first derivative of-x^2sin(x)+4xcos(x)+2sin(x) ?
The first derivative of-x^2sin(x)+4xcos(x)+2sin(x) is -x^2cos(x)-6xsin(x)+6cos(x)