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Popular Calculus >

derivative of x^3*cos(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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