What is (\partial)/(\partial x)(4arctan(3/x)) ?

The answer to (\partial)/(\partial x)(4arctan(3/x)) is -(12)/(9+x^2)

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(\partial)/(\partial x)(4arctan(3/x))

\frac{\partial}{\partial x} (4 arctan (\frac{3}{x}))

- \frac{12}{9 + x ^{2}}

Solution steps

\frac{\partial}{\partial x} (4 arctan (\frac{3}{x}))

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (arctan (\frac{3}{x}))

Apply the chain rule:

\frac{1}{( \frac{3}{x} ) ^{2} + 1} \frac{\partial}{\partial x} (\frac{3}{x})

= \frac{1}{( \frac{3}{x} ) ^{2} + 1} \frac{\partial}{\partial x} (\frac{3}{x})

\frac{\partial}{\partial x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

= 4 \cdot \frac{1}{( \frac{3}{x} ) ^{2} + 1} (- \frac{3}{x ^{2}})

Simplify

4 \cdot \frac{1}{( \frac{3}{x} ) ^{2} + 1} (- \frac{3}{x ^{2}}) : - \frac{12}{9 + x ^{2}}

= - \frac{12}{9 + x ^{2}}

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What is (\partial)/(\partial x)(4arctan(3/x)) ?
The answer to (\partial)/(\partial x)(4arctan(3/x)) is -(12)/(9+x^2)