What is (\partial)/(\partial x)(4ye^{5x^2-6y}) ?

The answer to (\partial)/(\partial x)(4ye^{5x^2-6y}) is 40e^{5x^2-6y}yx

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(\partial)/(\partial x)(4ye^{5x^2-6y})

\frac{\partial}{\partial x} (4 y e^{5 x^{2} - 6 y})

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

Solution steps

\frac{\partial}{\partial x} (4 y e^{5 x^{2} - 6 y})

Treat

y

as a constant

Take the constant out:

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

= 4 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

= 4 y e^{5 x^{2} - 6 y} \cdot 10 x

Simplify

= 40 e^{5 x^{2} - 6 y} y x

x \to 0 + lim (x^{\frac{1}{x}})

{\frac{1}{S ^{2} + 3 S}}

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

\frac{\partial}{\partial z} (2 x z)

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

What is (\partial)/(\partial x)(4ye^{5x^2-6y}) ?
The answer to (\partial)/(\partial x)(4ye^{5x^2-6y}) is 40e^{5x^2-6y}yx