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

The derivative of (ln(x))/(x^4) is (1-4ln(x))/(x^5)

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

The first derivative of (ln(x))/(x^4) is (1-4ln(x))/(x^5)

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derivative of

\frac{ln ( x )}{x ^{4}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{\frac{1}{x} x ^{4} - 4 x ^{3} ln ( x )}{( x ^{4} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{4} - 4 x ^{3} ln ( x )}{( x ^{4} ) ^{2}} : \frac{1 - 4 ln ( x )}{x ^{5}}

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

\int \frac{x}{x - 36} d x

y = 4 x - x^{2}

x \cdot sin (x) \cdot d x + cos (y) \cdot d y = 0

\int y^{2} - 2 y + 1 d y

\frac{\partial}{\partial v} (v cos (u))

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