What is the derivative of x^{-3}ln(x) ?

The derivative of x^{-3}ln(x) is (-3ln(x)+1)/(x^4)

What is the first derivative of x^{-3}ln(x) ?

The first derivative of x^{-3}ln(x) is (-3ln(x)+1)/(x^4)

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\frac{d}{d x} (x^{- 3} ln (x))

\frac{- 3 ln ( x ) + 1}{x ^{4}}

Solution steps

\frac{d}{d x} (x^{- 3} ln (x))

Apply the Product Rule:

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

f = x^{- 3}, g = ln (x)

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

\frac{d}{d x} (x^{- 3}) = - \frac{3}{x ^{4}}

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

= (- \frac{3}{x ^{4}}) ln (x) + \frac{1}{x} x^{- 3}

Simplify

(- \frac{3}{x ^{4}}) ln (x) + \frac{1}{x} x^{- 3} : \frac{- 3 ln ( x ) + 1}{x ^{4}}

= \frac{- 3 ln ( x ) + 1}{x ^{4}}

\int_{0}^{3} 2 x d x

x \to \frac{1}{2} π lim (tan (x))

t \frac{d y}{d t} = t^{3} + 19 t^{3} y

s^{2}

x \to (- 1) + lim (x + 1)

What is the derivative of x^{-3}ln(x) ?
The derivative of x^{-3}ln(x) is (-3ln(x)+1)/(x^4)
What is the first derivative of x^{-3}ln(x) ?
The first derivative of x^{-3}ln(x) is (-3ln(x)+1)/(x^4)