What is (\partial)/(\partial x)(2ye^{2xy}) ?

The answer to (\partial)/(\partial x)(2ye^{2xy}) is 4e^{2yx}y^2

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(\partial)/(\partial x)(2ye^{2xy})

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

4 e^{2 y x} y^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x y) = 2 y

= 2 y e^{2 x y} \cdot 2 y

Simplify

2 y e^{2 x y} \cdot 2 y : 4 e^{2 y x} y^{2}

= 4 e^{2 y x} y^{2}

f (x) = \frac{x}{1 - ln ( x - 6 )}

2 x + 2 y \frac{d y}{d x} = 0

\int_{0}^{5 r} 2 (25 r^{2} - y^{2}) d y

\int \frac{1}{y ^{3} + 1} d y

y = 6 tan (x), at x = \frac{π}{3}

What is (\partial)/(\partial x)(2ye^{2xy}) ?
The answer to (\partial)/(\partial x)(2ye^{2xy}) is 4e^{2yx}y^2