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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{5 x + 1}{4 x ^{2} + 1})

\frac{d}{d x} (lo g_{6} (5 x + 1))

\frac{d}{d x} ((arcsin (x)) d x)

\int \frac{1}{9 x ^{2} + 18 x + 10} d x

f (x) = \frac{x + 1}{x - 1}

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