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Popular >

derivative of x^2cos(2x)

Solution

derivative of

x^{2} cos (2 x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

Popular Examples

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\frac{d}{d x} (lo g_{3} (x^{2}))

limit as x approaches 0 of 1/(ln(x^3))

x \to 0 lim (\frac{1}{ln ( x ^{3} )})

integral of 9+sin(x)

\int 9 + sin (x) d x

Frequently Asked Questions (FAQ)

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