What is the derivative of ((a+bx^n/(a-bx^n))^m) ?

The derivative of ((a+bx^n/(a-bx^n))^m) is (2abnmx^{n-1}(a+bx^n)^{m-1})/((a-bx^n)^{m+1)}

What is the first derivative of ((a+bx^n/(a-bx^n))^m) ?

The first derivative of ((a+bx^n/(a-bx^n))^m) is (2abnmx^{n-1}(a+bx^n)^{m-1})/((a-bx^n)^{m+1)}

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\frac{d}{d x} ((\frac{a + b x ^{n}}{a - b x ^{n}})^{m})

\frac{2 abnm x ^{n - 1} ( a + b x ^{n} ) ^{m - 1}}{( a - b x ^{n} ) ^{m + 1}}

Solution steps

\frac{d}{d x} ((\frac{a + b x ^{n}}{a - b x ^{n}})^{m})

Apply the chain rule:

m (\frac{a + b x ^{n}}{a - b x ^{n}})^{m - 1} \frac{d}{d x} (\frac{a + b x ^{n}}{a - b x ^{n}})

= m (\frac{a + b x ^{n}}{a - b x ^{n}})^{m - 1} \frac{d}{d x} (\frac{a + b x ^{n}}{a - b x ^{n}})

\frac{d}{d x} (\frac{a + b x ^{n}}{a - b x ^{n}}) = \frac{2 abn x ^{n - 1}}{( a - b x ^{n} ) ^{2}}

= m (\frac{a + b x ^{n}}{a - b x ^{n}})^{m - 1} \frac{2 abn x ^{n - 1}}{( a - b x ^{n} ) ^{2}}

Simplify

m (\frac{a + b x ^{n}}{a - b x ^{n}})^{m - 1} \frac{2 abn x ^{n - 1}}{( a - b x ^{n} ) ^{2}} : \frac{2 abnm x ^{n - 1} ( a + b x ^{n} ) ^{m - 1}}{( a - b x ^{n} ) ^{m + 1}}

= \frac{2 abnm x ^{n - 1} ( a + b x ^{n} ) ^{m - 1}}{( a - b x ^{n} ) ^{m + 1}}

What is the derivative of ((a+bx^n/(a-bx^n))^m) ?
The derivative of ((a+bx^n/(a-bx^n))^m) is (2abnmx^{n-1}(a+bx^n)^{m-1})/((a-bx^n)^{m+1)}
What is the first derivative of ((a+bx^n/(a-bx^n))^m) ?
The first derivative of ((a+bx^n/(a-bx^n))^m) is (2abnmx^{n-1}(a+bx^n)^{m-1})/((a-bx^n)^{m+1)}