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Popular >

derivative of xe^{x-y}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

derivative of csc^2(x-5)

\frac{d}{d x} (csc^{2} (x) - 5)

integral of ((8+5x))/(1+x^2)

\int \frac{( 8 + 5 x )}{1 + x ^{2}} d x

derivative of [x+(x+sin^2(x)^6]^3)

\frac{d}{d x} ([x + (x + sin^{2} (x))^{6}]^{3})

(\partial)/(\partial y)(xe^{xy+1})

\frac{\partial}{\partial y} (x e^{x y + 1})

integral from-1 to x^3 of sqrt(2+t^2)

\int_{- 1}^{x^{3}} 2 + t^{2} d t

Frequently Asked Questions (FAQ)

What is the derivative of xe^{x-y} ?
The derivative of xe^{x-y} is e^{x-y}+e^{x-y}x(1-(dy)/(dx))
What is the first derivative of xe^{x-y} ?
The first derivative of xe^{x-y} is e^{x-y}+e^{x-y}x(1-(dy)/(dx))