What is (\partial)/(\partial x)(5e^{x-y}) ?

The answer to (\partial)/(\partial x)(5e^{x-y}) is 5e^{x-y}

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(\partial)/(\partial x)(5e^{x-y})

\frac{\partial}{\partial x} (5 e^{x - y})

5 e^{x - y}

Solution steps

\frac{\partial}{\partial x} (5 e^{x - y})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial x} (e^{x - y})

Apply the chain rule:

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

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

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

= 5 e^{x - y} \cdot 1

Simplify

= 5 e^{x - y}

\int \frac{3}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\int \frac{2 u}{1 + u ^{2}} d u

y^{^{''}} + y^{^{'}} - 2 y = 2 x

\int 2 e^{u} d u

\frac{( 3 y ^{2} - x ^{2} )}{y ^{5}} y^{^{'}} + \frac{x}{2 y ^{4}} = 0

What is (\partial)/(\partial x)(5e^{x-y}) ?
The answer to (\partial)/(\partial x)(5e^{x-y}) is 5e^{x-y}