What is the derivative of y=(x^{-2})ln(x) ?

The derivative of y=(x^{-2})ln(x) is (-2ln(x)+1)/(x^3)

What is the first derivative of y=(x^{-2})ln(x) ?

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

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derivative of

y = (x^{- 2}) ln (x)

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

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

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

Simplify

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

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

\frac{d}{d t} (4 cos^{3} (t))

\frac{( 1 )}{( x ^{n} + a ^{n} )}

sin^{2} (x) (cos (x))^{2}

5 x^{2} y^{2}

\frac{- 2 y}{x}

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