What is the derivative of ((ax+b/(c^2+a))^{10}) ?

The derivative of ((ax+b/(c^2+a))^{10}) is (10a(ax+b)^9)/((c^2+a)^{10)}

What is the first derivative of ((ax+b/(c^2+a))^{10}) ?

The first derivative of ((ax+b/(c^2+a))^{10}) is (10a(ax+b)^9)/((c^2+a)^{10)}

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

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

Solution steps

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

Apply the chain rule:

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}

Simplify

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}}

What is the derivative of ((ax+b/(c^2+a))^{10}) ?
The derivative of ((ax+b/(c^2+a))^{10}) is (10a(ax+b)^9)/((c^2+a)^{10)}
What is the first derivative of ((ax+b/(c^2+a))^{10}) ?
The first derivative of ((ax+b/(c^2+a))^{10}) is (10a(ax+b)^9)/((c^2+a)^{10)}