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Popular >

derivative of 2x^2cos(2x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 2 \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)

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

Simplify

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

Popular Examples

tangent of y=2cos(x),\at x= pi/3 tangent of

y = 2 cos (x), at x = \frac{π}{3}

tangent of y^2+5x=x^2y-5,(3,5)tangent of

y^{2} + 5 x = x^{2} y - 5, (3, 5)

area x=y^2,x=3-2y^2 area

x = y^{2}, x = 3 - 2 y^{2}

derivative of x^4sqrt(x)

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

integral of (3x)/(sqrt(x^4+6x^2+5))

\int \frac{3 x}{x ^{4} + 6 x ^{2} + 5} d x

Frequently Asked Questions (FAQ)

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