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Popular Calculus >

derivative of x^2ln|x|

Solution

\frac{d}{d x} (x^{2} ln ∣ x ∣)

Solution

2 x ln ∣ x ∣ + x

Solution steps

\frac{d}{d x} (x^{2} ln ∣ x ∣)

Apply the Product Rule:

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

f = x^{2}, g = ln ∣ x ∣

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

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

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

= 2 x ln ∣ x ∣ + \frac{1}{x} x^{2}

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

= 2 x ln ∣ x ∣ + x

Graph

Popular Examples

derivative of f(x)=(x^2+2x)/((x+1)^2)

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x}{( x + 1 ) ^{2}}

(\partial)/(\partial x)(4e^{yz}cos(xyz))

\frac{\partial}{\partial x} (4 e^{yz} cos (x yz))

limit as x approaches 7 of (-2)/(7-x)

x \to 7 lim (\frac{- 2}{7 - x})

tangent of y=(6x)/(x+2),(4,4)

t an g e n t y = \frac{6 x}{x + 2}, (4, 4)

integral of ((x-2))/(x^2-7x+12)

\int \frac{( x - 2 )}{x ^{2} - 7 x + 12} d x

Frequently Asked Questions (FAQ)

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