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Popular >

derivative of 2x^3cos(3x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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