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Popular >

derivative of x^2ln(x^2)

Solution

derivative of

x^{2} ln (x^{2})

Solution

2 x ln (x^{2}) + 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}

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

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

Popular Examples

limit as x approaches 0 of \sqrt[2x]{a}

derivative of y=(5x+4)^3 derivative of

y = (5 x + 4)^{3}

1 - y^{^{'}} = cos (y)

integral from 2 to 3 of 3/(sqrt(3-x))

\int_{2}^{3} \frac{3}{3 - x} d x

area x=0,y=-1+(x^2)/4 ,y=2+x/4 area

x = 0, y = - 1 + \frac{x ^{2}}{4}, y = 2 + \frac{x}{4}

Frequently Asked Questions (FAQ)

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