What is the derivative of 3x^2cos(x-x^3sin(x)) ?

The derivative of 3x^2cos(x-x^3sin(x)) is 6xcos(x)-6x^2sin(x)-x^3cos(x)

What is the first derivative of 3x^2cos(x-x^3sin(x)) ?

The first derivative of 3x^2cos(x-x^3sin(x)) is 6xcos(x)-6x^2sin(x)-x^3cos(x)

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\frac{d}{d x} (3 x^{2} cos (x) - x^{3} sin (x))

6 x cos (x) - 6 x^{2} sin (x) - x^{3} cos (x)

Solution steps

\frac{d}{d x} (3 x^{2} cos (x) - x^{3} sin (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{2} cos (x)) - \frac{d}{d x} (x^{3} sin (x))

\frac{d}{d x} (3 x^{2} cos (x)) = 3 (2 x cos (x) - x^{2} sin (x))

\frac{d}{d x} (x^{3} sin (x)) = 3 x^{2} sin (x) + cos (x) x^{3}

= 3 (2 x cos (x) - x^{2} sin (x)) - (3 x^{2} sin (x) + cos (x) x^{3})

Simplify

3 (2 x cos (x) - x^{2} sin (x)) - (3 x^{2} sin (x) + cos (x) x^{3}) : 6 x cos (x) - 6 x^{2} sin (x) - x^{3} cos (x)

= 6 x cos (x) - 6 x^{2} sin (x) - x^{3} cos (x)

What is the derivative of 3x^2cos(x-x^3sin(x)) ?
The derivative of 3x^2cos(x-x^3sin(x)) is 6xcos(x)-6x^2sin(x)-x^3cos(x)
What is the first derivative of 3x^2cos(x-x^3sin(x)) ?
The first derivative of 3x^2cos(x-x^3sin(x)) is 6xcos(x)-6x^2sin(x)-x^3cos(x)