derivative of ((x^2-5^3)/(125))

Lösung

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})

\frac{6 x ( x ^{2} - 5 ) ^{2}}{125}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})

Entferne die Konstante:

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

= \frac{1}{125} \frac{d}{d x} ((x^{2} - 5)^{3})

Wende die Kettenregel an:

3 (x^{2} - 5)^{2} \frac{d}{d x} (x^{2} - 5)

= 3 (x^{2} - 5)^{2} \frac{d}{d x} (x^{2} - 5)

\frac{d}{d x} (x^{2} - 5) = 2 x

= \frac{1}{125} \cdot 3 (x^{2} - 5)^{2} \cdot 2 x

Vereinfache

\frac{1}{125} \cdot 3 (x^{2} - 5)^{2} \cdot 2 x : \frac{6 x ( x ^{2} - 5 ) ^{2}}{125}

= \frac{6 x ( x ^{2} - 5 ) ^{2}}{125}

x \to \infty lim (\frac{k}{x})

\int (x)^{\frac{3}{2}} d x

y^{^{''}} + y = csc^{2} (x)

\int x (x^{2} + 1)^{4} d x

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