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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

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