What is the derivative of xe^{-x^2y} ?

The derivative of xe^{-x^2y} is e^{-x^2y}+e^{-x^2y}x(-2xy-x^2(dy)/(dx))

What is the first derivative of xe^{-x^2y} ?

The first derivative of xe^{-x^2y} is e^{-x^2y}+e^{-x^2y}x(-2xy-x^2(dy)/(dx))

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Popular >

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

e^{- x^{2} y} + e^{- x^{2} y} x (- 2 x y - x^{2} \frac{d y}{d x})

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- x^{2} y}

= \frac{d x}{d x} e^{- x^{2} y} + \frac{d}{d x} (e^{- x^{2} y}) x

\frac{d x}{d x} = 1

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

= 1 \cdot e^{- x^{2} y} + e^{- x^{2} y} (- 2 x y - x^{2} \frac{d y}{d x}) x

Simplify

= e^{- x^{2} y} + e^{- x^{2} y} x (- 2 x y - x^{2} \frac{d y}{d x})

\frac{d ^{2}}{d x ^{2}} (3 x sin (x^{2}))

\int \frac{x}{x - 9} d x

\int \frac{1}{x x ^{3} - 1} d x

\int \frac{- 3}{x ^{2}} + 11 - 4^{x} d x

sin^{5} (x^{3})

What is the derivative of xe^{-x^2y} ?
The derivative of xe^{-x^2y} is e^{-x^2y}+e^{-x^2y}x(-2xy-x^2(dy)/(dx))
What is the first derivative of xe^{-x^2y} ?
The first derivative of xe^{-x^2y} is e^{-x^2y}+e^{-x^2y}x(-2xy-x^2(dy)/(dx))