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

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

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

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

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derivative of

cos (x) x^{3}

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

Solution steps

\frac{d}{d x} (cos (x) x^{3})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = x^{3}

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

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

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

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

Simplify

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

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