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

The answer to (\partial)/(\partial x)(5xye^{-y^2}) is 5e^{-y^2}y

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (x) = 1

= 5 y e^{- y^{2}} \cdot 1

Simplify

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

\int (\frac{15}{x ^{4}} + \frac{8}{x ^{5}}) d x

\frac{d}{d x} (\frac{sin ( 3 x )}{x})

6 y^{^{''}} + 8 y^{^{'}} + y = 0, y (- 2) = - 3, y^{^{'}} (- 2) = - 4

\int \frac{7 x + 1}{6 x ^{2} + x - 1} d x

x \to 4 lim (- \frac{15}{x - 4})

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