What is (\partial)/(\partial x)(arctan(y^3x)) ?

The answer to (\partial)/(\partial x)(arctan(y^3x)) is (y^3)/(y^6x^2+1)

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(\partial)/(\partial x)(arctan(y^3x))

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

\frac{y ^{3}}{y ^{6} x ^{2} + 1}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( y ^{3} x ) ^{2} + 1} y^{3} : \frac{y ^{3}}{y ^{6} x ^{2} + 1}

= \frac{y ^{3}}{y ^{6} x ^{2} + 1}

\int \frac{x}{9 + x ^{2}} d x

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

\frac{\partial}{\partial y} (\frac{x ^{2}}{4 - y ^{2}})

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

\frac{1}{d + k e ^{d}}

What is (\partial)/(\partial x)(arctan(y^3x)) ?
The answer to (\partial)/(\partial x)(arctan(y^3x)) is (y^3)/(y^6x^2+1)