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Beliebt Rechnen >

(\partial)/(\partial x)(1/(ln(x-y)))

Lösung

\frac{\partial}{\partial x} (\frac{1}{ln ( x - y )})

Lösung

- \frac{1}{ln ^{2} ( x - y ) ( x - y )}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{ln ( x - y )})

Behandle

y

als Konstante

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial x} (ln^{- 1} (x - y))

Wende die Kettenregel an:

- \frac{1}{( ln ( x - y ) ) ^{2}} \frac{\partial}{\partial x} (ln (x - y))

= - \frac{1}{( ln ( x - y ) ) ^{2}} \frac{\partial}{\partial x} (ln (x - y))

\frac{\partial}{\partial x} (ln (x - y)) = \frac{1}{x - y}

= - \frac{1}{( ln ( x - y ) ) ^{2}} \cdot \frac{1}{x - y}

Vereinfache

- \frac{1}{ln ^{2} ( x - y )} \cdot \frac{1}{x - y} : - \frac{1}{ln ^{2} ( x - y ) ( x - y )}

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

Beliebte Beispiele

sum from n=1 to infinity of 1/(n^{0.3)}

n = 1 \sum \infty \frac{1}{n ^{0.3}}

integral of-e^{-y}

\int - e^{- y} d y

derivative f(x)=x^2*sin(x)

d er i v a t i v e f (x) = x^{2} \cdot sin (x)

derivative of ((x^3-1)/((x^3+1)))

\frac{d}{d x} (\frac{( x ^{3} - 1 )}{( x ^{3} + 1 )})

tangent y=0.03x^2+1

t an g e n t y = 0.03 x^{2} + 1