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Popular >

derivative of x^2ln^2(x)

Solution

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

Solution

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

Solution steps

\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)

= \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{2 ln ( x )}{x}

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

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

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

Graph

Popular Examples

sum from n=0 to infinity of e^{-(5n)/2}

n = 0 \sum \infty e^{- \frac{5 n}{2}}

(\partial)/(\partial x)(x^3e^y+cos(y))

\frac{\partial}{\partial x} (x^{3} e^{y} + cos (y))

integral from 1 to e^2 of x^2ln(x)

\int_{1}^{e^{2}} x^{2} ln (x) d x

derivative of (x+4)/(x^3+x-5)derivative of

\frac{x + 4}{x ^{3} + x - 5}

area y=2x,x=5,y= 2/x area

y = 2 x, x = 5, y = \frac{2}{x}

Frequently Asked Questions (FAQ)

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