What is the derivative of (ln(x)/(x^8)) ?

The derivative of (ln(x)/(x^8)) is (1-8ln(x))/(x^9)

What is the first derivative of (ln(x)/(x^8)) ?

The first derivative of (ln(x)/(x^8)) is (1-8ln(x))/(x^9)

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\frac{d}{d x} (\frac{ln ( x )}{x ^{8}})

\frac{1 - 8 ln ( x )}{x ^{9}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{8}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{8} - \frac{d}{d x} ( x ^{8} ) ln ( x )}{( x ^{8} ) ^{2}}

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{\frac{1}{x} x ^{8} - 8 x ^{7} ln ( x )}{( x ^{8} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{8} - 8 x ^{7} ln ( x )}{( x ^{8} ) ^{2}} : \frac{1 - 8 ln ( x )}{x ^{9}}

= \frac{1 - 8 ln ( x )}{x ^{9}}

\frac{\partial}{\partial x} (\frac{47 x y}{x - y})

\frac{d}{d x} (sec (x) csc (x))

x, 1 - x, - \frac{x}{2}

\int ln ∣ x ∣ sin (x) d x

What is the derivative of (ln(x)/(x^8)) ?
The derivative of (ln(x)/(x^8)) is (1-8ln(x))/(x^9)
What is the first derivative of (ln(x)/(x^8)) ?
The first derivative of (ln(x)/(x^8)) is (1-8ln(x))/(x^9)