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Popular >

derivative of 2x^2ln(2x)

Solution

derivative of

2 x^{2} ln (2 x)

Solution

2 (2 x ln (2 x) + x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

= 2 (2 x ln (2 x) + \frac{1}{x} x^{2})

\frac{1}{x} x^{2} = x

= 2 (2 x ln (2 x) + x)

Popular Examples

(\partial)/(\partial x)(cos^2(2x))

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

limit as x approaches 0 of-cos(1/x)

x \to 0 lim (- cos (\frac{1}{x}))

tangent of f(x)=4x^2+2x,\at x=2 tangent of

f (x) = 4 x^{2} + 2 x, at x = 2

(\partial)/(\partial x)(sech^2(x-t))

\frac{\partial}{\partial x} (sech^{2} (x - t))

integral of x^3cos(x^4+2)

\int x^{3} cos (x^{4} + 2) d x

Frequently Asked Questions (FAQ)

What is the derivative of 2x^2ln(2x) ?
The derivative of 2x^2ln(2x) is 2(2xln(2x)+x)
What is the first derivative of 2x^2ln(2x) ?
The first derivative of 2x^2ln(2x) is 2(2xln(2x)+x)