What is the derivative of (1-4ln(x)/(x^5)) ?

The derivative of (1-4ln(x)/(x^5)) is -(-20ln(x)+9)/(x^6)

What is the first derivative of (1-4ln(x)/(x^5)) ?

The first derivative of (1-4ln(x)/(x^5)) is -(-20ln(x)+9)/(x^6)

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

- \frac{- 20 ln ( x ) + 9}{x ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

Simplify

\frac{( - \frac{4}{x} ) x ^{5} - 5 x ^{4} ( 1 - 4 ln ( x ) )}{( x ^{5} ) ^{2}} : - \frac{- 20 ln ( x ) + 9}{x ^{6}}

= - \frac{- 20 ln ( x ) + 9}{x ^{6}}

sin (2 π t)

\frac{d}{d y} (\frac{350}{x ^{2} + y ^{2}})

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

f (x) = x^{\frac{1}{2}}, (81, 9)

\int \frac{ln ( x )}{5 x ^{4}} d x

What is the derivative of (1-4ln(x)/(x^5)) ?
The derivative of (1-4ln(x)/(x^5)) is -(-20ln(x)+9)/(x^6)
What is the first derivative of (1-4ln(x)/(x^5)) ?
The first derivative of (1-4ln(x)/(x^5)) is -(-20ln(x)+9)/(x^6)