What is (\partial)/(\partial x)(arctan(xsqrt(y))) ?

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

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(\partial)/(\partial x)(arctan(xsqrt(y)))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 2 cos^{2} (x) d x

\frac{d}{d x} (cos (e^{x^{2} c o s (x)}))

n = 1 \sum \infty \frac{4 ^{n}}{5 ^{n}}

8 t^{2} - t

\frac{d}{d x} (5 e^{x^{3}})

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