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Popular >

derivative of x*ln^2(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

integral of 4cos(x)+9sin(x)

\int 4 cos (x) + 9 sin (x) d x

integral of 5/((3x+5)^4)

\int \frac{5}{( 3 x + 5 ) ^{4}} d x

derivative of f(x)=sqrt((4x+1)/(2x^2+1))derivative of

f (x) = \frac{4 x + 1}{2 x ^{2} + 1}

integral of (x-y)/(x+y)

\int \frac{x - y}{x + y} d y

integral of 9x^{1/2}

\int 9 x^{\frac{1}{2}} d x

Frequently Asked Questions (FAQ)

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