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Popular >

derivative of x^2*ln(x^2)

Solution

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

Solution

4 x ln (x) + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x ln (x^{2}) + \frac{2}{x} x^{2} : 4 x ln (x) + 2 x

= 4 x ln (x) + 2 x

Popular Examples

tangent of f(x)= 1/(x+6),\at x=3 tangent of

f (x) = \frac{1}{x + 6}, at x = 3

lcm x^3,2x-15.8x^2 lcm

x^{3}, 2 x - 15.8 x^{2}

limit as x approaches infinity of (1-1/x)^{x-1}

x \to \infty lim ((1 - \frac{1}{x})^{x - 1})

area sqrt(x-2),14-x,x=2 area

x - 2, 14 - x, x = 2

integral from 0 to 1 of (1-sqrt(x))^2

\int_{0}^{1} (1 - x)^{2} d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2*ln(x^2) ?
The derivative of x^2*ln(x^2) is 4xln(x)+2x
What is the first derivative of x^2*ln(x^2) ?
The first derivative of x^2*ln(x^2) is 4xln(x)+2x