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

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

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(\partial)/(\partial x)(e^x(x-y)^2)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

\int (x - 2) (2 x + 3) d x

x \frac{d y}{d x} = y ln (x y)

\frac{\partial}{\partial x} (sin (y) e^{x})

n = 0 \sum \infty \frac{3 ^{n}}{n}

\int_{0}^{2} - 3 x^{3} x^{2} + 4 d x

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