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Beliebt Rechnen >

derivative of ln(x-y^2)

Lösung

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

Lösung

\frac{1 - 2 y \frac{d y}{d x}}{x - y ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1 - 2 y \frac{d y}{d x}}{x - y ^{2}}

Beliebte Beispiele

integral of 1/(y(1-y))

\int \frac{1}{y ( 1 - y )} d y

integral of (1/(x^2-x))

\int (\frac{1}{x ^{2} - x}) d x

(dy)/(dx)=9e^{x-y}

\frac{d y}{d x} = 9 e^{x - y}

derivative f(x)=\sqrt[3]{x^7-4x}

d er i v a t i v e f (x) = 3 x^{7} - 4 x

derivative of sin(3x+cos(4x))

\frac{d}{d x} (sin (3 x) + cos (4 x))