What is the derivative of 2arctan(y/x) ?

The derivative of 2arctan(y/x) is (2(x\frac{dy)/(dx)-y)}{y^2+x^2}

What is the first derivative of 2arctan(y/x) ?

The first derivative of 2arctan(y/x) is (2(x\frac{dy)/(dx)-y)}{y^2+x^2}

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\frac{d}{d x} (2 arctan (\frac{y}{x}))

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

Solution steps

\frac{d}{d x} (2 arctan (\frac{y}{x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (arctan (\frac{y}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

(2) (1) \frac{d y}{d x} = 7

\int \frac{2 x - 1}{x} d x

x^{2} sin (4 x)

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 8 x^{7} y^{8})

\frac{\partial}{\partial x} (x arcsin (3 x))

What is the derivative of 2arctan(y/x) ?
The derivative of 2arctan(y/x) is (2(x\frac{dy)/(dx)-y)}{y^2+x^2}
What is the first derivative of 2arctan(y/x) ?
The first derivative of 2arctan(y/x) is (2(x\frac{dy)/(dx)-y)}{y^2+x^2}