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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\int x + 1 d x

\int sec^{2} (x) + sec (x) tan (x) d x

\int \frac{π}{2} (x + cos (x)) d x

\frac{d}{d x} (x^{2} - 4 x + 1)

\int tan (2) (x) d x

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