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Popular Calculus >

derivative of (cos(x)(2x^3))

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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}

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

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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