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

解

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

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

解答ステップ

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

連鎖法則を適用:

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}

簡素化

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}}