What is the derivative of 2cos(x-4xsin(x)-x^2cos(x)) ?

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{1}{3 s h x + 5 c h x} d x

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

\frac{d y}{d x} = 0.002 y (500 - y) - 80

\frac{d}{d x} (x - 16)

\int e^{- 0.1 t} d t

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