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Popular >

derivative of x(ln(x)^2)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{ln ( x ) - 1}{( ln ( x ) ) ^{2}} d x

limit as h approaches 0 of ((x+h)^{-5}-x^{-5})/h

h \to 0 lim (\frac{( x + h ) ^{- 5} - x ^{- 5}}{h})

integral of (sqrt(x))/(sqrt(x+1))

\int \frac{x}{x + 1} d x

t^2y^2+e^{1/t}+(2yt^3+t^2y^3)y^'=0

t^{2} y^{2} + e^{\frac{1}{t}} + (2 y t^{3} + t^{2} y^{3}) y^{^{'}} = 0

y^{''}+8y^'+25y=0

y^{^{''}} + 8 y^{^{'}} + 25 y = 0

Frequently Asked Questions (FAQ)

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