What is (\partial)/(\partial x)(2y*e^{5x^2-9y}) ?

The answer to (\partial)/(\partial x)(2y*e^{5x^2-9y}) is 20e^{5x^2-9y}yx

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(\partial)/(\partial x)(2y*e^{5x^2-9y})

\frac{\partial}{\partial x} (2 y \cdot e^{5 x^{2} - 9 y})

20 e^{5 x^{2} - 9 y} y x

Solution steps

\frac{\partial}{\partial x} (2 y e^{5 x^{2} - 9 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} - 9 y})

Apply the chain rule:

e^{5 x^{2} - 9 y} \frac{\partial}{\partial x} (5 x^{2} - 9 y)

= e^{5 x^{2} - 9 y} \frac{\partial}{\partial x} (5 x^{2} - 9 y)

\frac{\partial}{\partial x} (5 x^{2} - 9 y) = 10 x

= 2 y e^{5 x^{2} - 9 y} \cdot 10 x

Simplify

= 20 e^{5 x^{2} - 9 y} y x

\int 11 x^{3} e^{x} d x

\int csc^{13} (x) d x

g (x) = \frac{4}{2 - x}, y = 4, x = 0

\frac{\partial}{\partial x} (x + y^{4})

\frac{d}{d x} ((2 x^{3} + 3 x - 1)^{4})

What is (\partial)/(\partial x)(2y*e^{5x^2-9y}) ?
The answer to (\partial)/(\partial x)(2y*e^{5x^2-9y}) is 20e^{5x^2-9y}yx