What is the derivative of (-2x+3x^{-2}ln(x)) ?

The derivative of (-2x+3x^{-2}ln(x)) is -2ln(x)+(-6ln(x)-2x^3+3)/(x^3)

What is the first derivative of (-2x+3x^{-2}ln(x)) ?

The first derivative of (-2x+3x^{-2}ln(x)) is -2ln(x)+(-6ln(x)-2x^3+3)/(x^3)

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

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

Solution steps

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

Apply the Product Rule:

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

f = - 2 x + 3 x^{- 2}, g = ln (x)

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

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

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

= (- 2 - \frac{6}{x ^{3}}) ln (x) + \frac{1}{x} (- 2 x + 3 x^{- 2})

Simplify

(- 2 - \frac{6}{x ^{3}}) ln (x) + \frac{1}{x} (- 2 x + 3 x^{- 2}) : - 2 ln (x) + \frac{- 6 ln ( x ) - 2 x ^{3} + 3}{x ^{3}}

= - 2 ln (x) + \frac{- 6 ln ( x ) - 2 x ^{3} + 3}{x ^{3}}

\frac{d}{d x} (\frac{x ^{7}}{x ^{4}})

x \to 0 lim (1 + \frac{1}{x ^{2}})

x^{3} - 2 x^{2} y - 2 y^{2} - 1

arcsin (\frac{x}{7})

y = 4^{- x} sin (x)

What is the derivative of (-2x+3x^{-2}ln(x)) ?
The derivative of (-2x+3x^{-2}ln(x)) is -2ln(x)+(-6ln(x)-2x^3+3)/(x^3)
What is the first derivative of (-2x+3x^{-2}ln(x)) ?
The first derivative of (-2x+3x^{-2}ln(x)) is -2ln(x)+(-6ln(x)-2x^3+3)/(x^3)