What is (\partial)/(\partial x)(2ye^{5x^2-6y}) ?

The answer to (\partial)/(\partial x)(2ye^{5x^2-6y}) is 20e^{5x^2-6y}yx

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(\partial)/(\partial x)(2ye^{5x^2-6y})

\frac{\partial}{\partial x} (2 y e^{5 x^{2} - 6 y})

20 e^{5 x^{2} - 6 y} y x

Solution steps

\frac{\partial}{\partial x} (2 y e^{5 x^{2} - 6 y})

Treat

y

as a constant

Take the constant out:

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

= 2 y \frac{\partial}{\partial x} (e^{5 x^{2} - 6 y})

Apply the chain rule:

e^{5 x^{2} - 6 y} \frac{\partial}{\partial x} (5 x^{2} - 6 y)

= e^{5 x^{2} - 6 y} \frac{\partial}{\partial x} (5 x^{2} - 6 y)

\frac{\partial}{\partial x} (5 x^{2} - 6 y) = 10 x

= 2 y e^{5 x^{2} - 6 y} \cdot 10 x

Simplify

= 20 e^{5 x^{2} - 6 y} y x

What is (\partial)/(\partial x)(2ye^{5x^2-6y}) ?
The answer to (\partial)/(\partial x)(2ye^{5x^2-6y}) is 20e^{5x^2-6y}yx