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Beliebt Rechnen >

(\partial)/(\partial x)(5ln(1+x^2-y))

Lösung

\frac{\partial}{\partial x} (5 ln (1 + x^{2} - y))

Lösung

\frac{10 x}{1 + x ^{2} - y}

Schritte zur Lösung

\frac{\partial}{\partial x} (5 ln (1 + x^{2} - y))

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial x} (ln (1 + x^{2} - y))

Wende die Kettenregel an:

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

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

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

= 5 \cdot \frac{1}{1 + x ^{2} - y} \cdot 2 x

Vereinfache

5 \cdot \frac{1}{1 + x ^{2} - y} \cdot 2 x : \frac{10 x}{1 + x ^{2} - y}

= \frac{10 x}{1 + x ^{2} - y}

Beliebte Beispiele

limit as x approaches 0 of (ln(x))/(x^2)

x \to 0 lim (\frac{ln ( x )}{x ^{2}})

integral of 1/(sqrt(1+x+x^2))

\int \frac{1}{1 + x + x ^{2}} d x

f^'(x)=5(1+e^x)^4e^x

f^{^{'}} (x) = 5 (1 + e^{x})^{4} e^{x}

derivative h(w)=(5w^3-w)/w

d er i v a t i v e h (w) = \frac{5 w ^{3} - w}{w}

derivative of (x^2-3^4)

\frac{d}{d x} ((x^{2} - 3)^{4})