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Popular >

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

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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