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

The derivative of (ln(x)/(x^5)) is (1-5ln(x))/(x^6)

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

The first derivative of (ln(x)/(x^5)) is (1-5ln(x))/(x^6)

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

\frac{1 - 5 ln ( x )}{x ^{6}}

Solution steps

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

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

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

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

Simplify

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

= \frac{1 - 5 ln ( x )}{x ^{6}}

e^{l n (x)}

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

\frac{d}{d x} (\frac{sin ^{2} ( x )}{x})

\frac{1}{3} x^{3} + 8 x^{2} + 63 x + 7

\int_{- 4 π}^{4 π} sin^{2} (x) + 1 d x

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