What is the derivative of y=(ln(x))/(x^9) ?

The derivative of y=(ln(x))/(x^9) is (1-9ln(x))/(x^{10)}

What is the first derivative of y=(ln(x))/(x^9) ?

The first derivative of y=(ln(x))/(x^9) is (1-9ln(x))/(x^{10)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{ln ( x )}{x ^{9}}

\frac{1 - 9 ln ( x )}{x ^{10}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{9}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{9} - \frac{d}{d x} ( x ^{9} ) ln ( x )}{( x ^{9} ) ^{2}}

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

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

Simplify

\frac{\frac{1}{x} x ^{9} - 9 x ^{8} ln ( x )}{( x ^{9} ) ^{2}} : \frac{1 - 9 ln ( x )}{x ^{10}}

= \frac{1 - 9 ln ( x )}{x ^{10}}

\int \frac{1}{2} ln (x) d x

\frac{d}{d x} (- 8 e^{- x})

4 x^{^{''}} + 2 x^{^{'}} + 4 x = 100, x (0) = 5, x^{^{'}} (0) = 0

x \to 3 lim (5 x^{2} + 2 x)

x \cdot \frac{d y}{d x} + y = e^{- x}

What is the derivative of y=(ln(x))/(x^9) ?
The derivative of y=(ln(x))/(x^9) is (1-9ln(x))/(x^{10)}
What is the first derivative of y=(ln(x))/(x^9) ?
The first derivative of y=(ln(x))/(x^9) is (1-9ln(x))/(x^{10)}