What is the derivative of (ln(-2x^3+5x^2)/(-x)) ?

The derivative of (ln(-2x^3+5x^2)/(-x)) is -(2(-3x+5)-ln(-2x^3+5x^2)(-2x+5))/(x^2(-2x+5))

What is the first derivative of (ln(-2x^3+5x^2)/(-x)) ?

The first derivative of (ln(-2x^3+5x^2)/(-x)) is -(2(-3x+5)-ln(-2x^3+5x^2)(-2x+5))/(x^2(-2x+5))

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

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

Solution steps

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

Simplify

\frac{ln ( - 2 x ^{3} + 5 x ^{2} )}{- x} : - \frac{ln ( - 2 x ^{3} + 5 x ^{2} )}{x}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

= - \frac{\frac{2 ( - 3 x + 5 )}{x ( - 2 x + 5 )} x - 1 \cdot ln ( - 2 x ^{3} + 5 x ^{2} )}{x ^{2}}

Simplify

- \frac{\frac{2 ( - 3 x + 5 )}{x ( - 2 x + 5 )} x - 1 \cdot ln ( - 2 x ^{3} + 5 x ^{2} )}{x ^{2}} : - \frac{2 ( - 3 x + 5 ) - ln ( - 2 x ^{3} + 5 x ^{2} ) ( - 2 x + 5 )}{x ^{2} ( - 2 x + 5 )}

= - \frac{2 ( - 3 x + 5 ) - ln ( - 2 x ^{3} + 5 x ^{2} ) ( - 2 x + 5 )}{x ^{2} ( - 2 x + 5 )}

f (x) = \frac{1}{1 + x}

x \to 1 lim (x^{3} - x + 2)

2 y^{^{''}} + y^{^{'}} - 4 y = 0

\int \frac{cos ( \frac{1}{x} )}{x} d x

\int \frac{4}{3} π r^{3} d r

What is the derivative of (ln(-2x^3+5x^2)/(-x)) ?
The derivative of (ln(-2x^3+5x^2)/(-x)) is -(2(-3x+5)-ln(-2x^3+5x^2)(-2x+5))/(x^2(-2x+5))
What is the first derivative of (ln(-2x^3+5x^2)/(-x)) ?
The first derivative of (ln(-2x^3+5x^2)/(-x)) is -(2(-3x+5)-ln(-2x^3+5x^2)(-2x+5))/(x^2(-2x+5))