What is the derivative of 1/(x^2ln(x)) ?

The derivative of 1/(x^2ln(x)) is -(2ln(x)+1)/(x^3ln^2(x))

What is the first derivative of 1/(x^2ln(x)) ?

The first derivative of 1/(x^2ln(x)) is -(2ln(x)+1)/(x^3ln^2(x))

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

- \frac{2 ln ( x ) + 1}{x ^{3} ln ^{2} ( x )}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ^{2} ln ( x ) ) ^{2}} (2 x ln (x) + x) : - \frac{2 ln ( x ) + 1}{x ^{3} ln ^{2} ( x )}

= - \frac{2 ln ( x ) + 1}{x ^{3} ln ^{2} ( x )}

f (x) = 7 x + 11, at x = 2

\frac{d y}{d x} = \frac{cos ( 8 x )}{e ^{8 y}}

g (x) = (5 - x)^{2} (2 x - 1)^{5}

\int_{- 8}^{10} \frac{x}{2} + 10 d x

\int \frac{y ^{2}}{4} d y

What is the derivative of 1/(x^2ln(x)) ?
The derivative of 1/(x^2ln(x)) is -(2ln(x)+1)/(x^3ln^2(x))
What is the first derivative of 1/(x^2ln(x)) ?
The first derivative of 1/(x^2ln(x)) is -(2ln(x)+1)/(x^3ln^2(x))