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Popular >

derivative of 2x^2cos(4x)

Solution

\frac{d}{d x} (2 x^{2} cos (4 x))

Solution

2 (2 x cos (4 x) - 4 x^{2} sin (4 x))

Solution steps

\frac{d}{d x} (2 x^{2} cos (4 x))

Take the constant out:

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

= 2 \frac{d}{d x} (x^{2} cos (4 x))

Apply the Product Rule:

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

f = x^{2}, g = cos (4 x)

= 2 (\frac{d}{d x} (x^{2}) cos (4 x) + \frac{d}{d x} (cos (4 x)) x^{2})

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= 2 (2 x cos (4 x) + (- sin (4 x) \cdot 4) x^{2})

Simplify

= 2 (2 x cos (4 x) - 4 x^{2} sin (4 x))

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\int - 5 ln (x^{2} - 1) d x

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\int (5 cos (x) - 2 sec^{2} (x)) d x

Frequently Asked Questions (FAQ)

What is the derivative of 2x^2cos(4x) ?
The derivative of 2x^2cos(4x) is 2(2xcos(4x)-4x^2sin(4x))
What is the first derivative of 2x^2cos(4x) ?
The first derivative of 2x^2cos(4x) is 2(2xcos(4x)-4x^2sin(4x))