What is the derivative of f(x)=arctan((1+x)/(1-x)) ?

The derivative of f(x)=arctan((1+x)/(1-x)) is 1/(x^2+1)

What is the first derivative of f(x)=arctan((1+x)/(1-x)) ?

The first derivative of f(x)=arctan((1+x)/(1-x)) is 1/(x^2+1)

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derivative of

f (x) = arctan (\frac{1 + x}{1 - x})

\frac{1}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (\frac{1 + x}{1 - x}))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x ^{2} + 1}

\frac{\partial}{\partial x} (1 + x^{3} + y^{4})

\int \frac{3 x + 4}{x + 3} d x

\int_{0}^{1} - 10 (x^{2} + 1) e^{- x} d x

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

\int x + 2 x d x d x

What is the derivative of f(x)=arctan((1+x)/(1-x)) ?
The derivative of f(x)=arctan((1+x)/(1-x)) is 1/(x^2+1)
What is the first derivative of f(x)=arctan((1+x)/(1-x)) ?
The first derivative of f(x)=arctan((1+x)/(1-x)) is 1/(x^2+1)