derivative of ((ax+b/(c^2+a))^{10})

Lösung

\frac{d}{d x} ((\frac{a x + b}{c ^{2} + a})^{10})

\frac{10 a ( a x + b ) ^{9}}{( c ^{2} + a ) ^{10}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{a x + b}{c ^{2} + a})^{10})

Wende die Kettenregel an:

10 (\frac{a x + b}{c ^{2} + a})^{9} \frac{d}{d x} (\frac{a x + b}{c ^{2} + a})

= 10 (\frac{a x + b}{c ^{2} + a})^{9} \frac{d}{d x} (\frac{a x + b}{c ^{2} + a})

\frac{d}{d x} (\frac{a x + b}{c ^{2} + a}) = \frac{a}{c ^{2} + a}

= 10 (\frac{a x + b}{c ^{2} + a})^{9} \frac{a}{c ^{2} + a}

Vereinfache

10 (\frac{a x + b}{c ^{2} + a})^{9} \frac{a}{c ^{2} + a} : \frac{10 a ( a x + b ) ^{9}}{( c ^{2} + a ) ^{10}}

= \frac{10 a ( a x + b ) ^{9}}{( c ^{2} + a ) ^{10}}

\int 5 e^{2} d x

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