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

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

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(\partial)/(\partial x)(4y*e^{5x^2-2y})

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int_{1}^{4} 1 + \frac{1}{x ^{2}} d x

\frac{d}{d t} (- 3 cos^{2} (t) sin (t))

\frac{x}{x ^{2} - 1}

x \to 5 lim (x^{2})

x \to \infty lim ((x)!)

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