What is the derivative of (x/(1+sqrt(1-x^2))^n) ?

The derivative of (x/(1+sqrt(1-x^2))^n) is (nx^{n-1})/((1+sqrt(1-x^2))^n\sqrt{-x^2+1)}

What is the first derivative of (x/(1+sqrt(1-x^2))^n) ?

The first derivative of (x/(1+sqrt(1-x^2))^n) is (nx^{n-1})/((1+sqrt(1-x^2))^n\sqrt{-x^2+1)}

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\frac{d}{d x} ((\frac{x}{1 + 1 - x ^{2}})^{n})

\frac{n x ^{n - 1}}{( 1 + 1 - x ^{2} ) ^{n} - x ^{2} + 1}

Solution steps

\frac{d}{d x} ((\frac{x}{1 + 1 - x ^{2}})^{n})

Apply the chain rule:

n (\frac{x}{1 + 1 - x ^{2}})^{n - 1} \frac{d}{d x} (\frac{x}{1 + 1 - x ^{2}})

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

\frac{d}{d x} (\frac{x}{1 + 1 - x ^{2}}) = \frac{1}{( - x ^{2} + 1 + 1 ) - x ^{2} + 1}

= n (\frac{x}{1 + 1 - x ^{2}})^{n - 1} \frac{1}{( - x ^{2} + 1 + 1 ) - x ^{2} + 1}

Simplify

n (\frac{x}{1 + 1 - x ^{2}})^{n - 1} \frac{1}{( - x ^{2} + 1 + 1 ) - x ^{2} + 1} : \frac{n x ^{n - 1}}{( 1 + 1 - x ^{2} ) ^{n} - x ^{2} + 1}

= \frac{n x ^{n - 1}}{( 1 + 1 - x ^{2} ) ^{n} - x ^{2} + 1}

f (x) = \frac{2 x}{1 - x}

\int_{4}^{x} \frac{( x - 4 ) ^{2}}{72} d x

x \to 1 lim (\frac{x}{x - 1} - \frac{1}{x})

\int \frac{x + 2}{x ^{2} + 4} d x

\frac{\partial}{\partial x} (7 x^{3 y})

What is the derivative of (x/(1+sqrt(1-x^2))^n) ?
The derivative of (x/(1+sqrt(1-x^2))^n) is (nx^{n-1})/((1+sqrt(1-x^2))^n\sqrt{-x^2+1)}
What is the first derivative of (x/(1+sqrt(1-x^2))^n) ?
The first derivative of (x/(1+sqrt(1-x^2))^n) is (nx^{n-1})/((1+sqrt(1-x^2))^n\sqrt{-x^2+1)}