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Popular >

derivative of x^3cos(2x)

Solution

derivative of

x^{3} cos (2 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = cos (2 x)

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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