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Popular Calculus >

derivative of (x^2/(ln(x)))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

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

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

Graph

Popular Examples

derivative of x^{3/5}sqrt(x^3+2x-6)

\frac{d}{d x} (x^{\frac{3}{5}} x^{3} + 2 x - 6)

derivative of 2x^2-9x+10

\frac{d}{d x} (2 x^{2} - 9 x + 10)

inverse oflaplace (2s-44)/(7s^2-14s+70)inverse laplace

\frac{2 s - 44}{7 s ^{2} - 14 s + 70}

(dx)/(dy)=((y-x))/(y+x)

\frac{d x}{d y} = \frac{( y - x )}{y + x}

area y=2,y=x^2+1 area

y = 2, y = x^{2} + 1

Frequently Asked Questions (FAQ)

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