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

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

Popular >

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

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

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

Solution steps

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

Treat

z, y

as constants

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\int \frac{1}{( 6 x - 1 ) ^{2}} d x

\frac{d}{d x} (- 16 x^{2})

\frac{\partial}{\partial z} (9 z e^{x yz})

\frac{d}{d x} ((1 + cos (x)) sin (x))

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