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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

- 36 sin (4 x)

s^{2} + 4 2 t + 1 + \frac{s}{r} + \frac{t ^{6} r ^{2}}{t + r ^{3}}

\int_{0}^{π} (cos (x)) d x

x \to 1 lim (\frac{x}{3 x + 2})

f (x) = 9 - 7 x

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