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

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

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(\partial)/(\partial x)((-y^2+x)e^{(x-y)})

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

e^{x - y} + e^{x - y} (- y^{2} + x)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (- y^{2} + x) = 1

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

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

Simplify

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

f (x) = 2 x^{2} - 196 ln (x)

\int \frac{1}{( 16 - t ^{2} ) ^{\frac{3}{2}}} d t

\int_{- 1}^{3} 30 - 3 y^{2} - \frac{9}{2} d y

\frac{d y}{d x} = \frac{1}{1 + x ^{2}}

x \to 0 lim (\frac{5}{1 - e ^{\frac{1}{x}}})

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