What is the derivative of (4-x/(5x)) ?

The derivative of (4-x/(5x)) is -4/(5x^2)

What is the first derivative of (4-x/(5x)) ?

The first derivative of (4-x/(5x)) is -4/(5x^2)

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\frac{d}{d x} (\frac{4 - x}{5 x})

- \frac{4}{5 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 - x}{5 x})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{4 - x}{x})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( 4 - x ) x - \frac{d x}{d x} ( 4 - x )}{x ^{2}}

\frac{d}{d x} (4 - x) = - 1

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

= \frac{1}{5} \cdot \frac{( - 1 ) x - 1 \cdot ( 4 - x )}{x ^{2}}

Simplify

\frac{1}{5} \cdot \frac{( - 1 ) x - 1 \cdot ( 4 - x )}{x ^{2}} : - \frac{4}{5 x ^{2}}

= - \frac{4}{5 x ^{2}}

\int \frac{( ln ( x ) ) ^{32}}{x} d x

x \to 2 lim (2 x^{4} - 10)

\frac{\partial}{\partial y} (y^{5} - 3 x y)

\frac{d ^{2}}{d x ^{2}} (ln (x^{2} + 3 x + 15))

f (x) = 8 ln (x)

What is the derivative of (4-x/(5x)) ?
The derivative of (4-x/(5x)) is -4/(5x^2)
What is the first derivative of (4-x/(5x)) ?
The first derivative of (4-x/(5x)) is -4/(5x^2)