What is (\partial)/(\partial x)((xe^y)/(3z^2+1)) ?

The answer to (\partial)/(\partial x)((xe^y)/(3z^2+1)) is (e^y)/(3z^2+1)

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(\partial)/(\partial x)((xe^y)/(3z^2+1))

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

\frac{e ^{y}}{3 z ^{2} + 1}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= \frac{e ^{y}}{3 z ^{2} + 1} \cdot 1

Simplify

= \frac{e ^{y}}{3 z ^{2} + 1}

\frac{d y}{d x} + 3 x y^{3} = 0, y (0) = 1

\int \frac{5 e ^{2 x} - e ^{x}}{e ^{2 x} - 1} d x

\frac{\partial}{\partial x} (9 x^{2} y^{2})

\int (x^{2} e^{2 x} - 3 x e^{2 x} + 5 e^{2 x}) d x

What is (\partial)/(\partial x)((xe^y)/(3z^2+1)) ?
The answer to (\partial)/(\partial x)((xe^y)/(3z^2+1)) is (e^y)/(3z^2+1)