What is (\partial)/(\partial x)(e^x*y*dy) ?

The answer to (\partial)/(\partial x)(e^x*y*dy) is y^2de^x

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(\partial)/(\partial x)(e^xydy)

\frac{\partial}{\partial x} (e^{x} \cdot y \cdot d y)

y^{2} d e^{x}

Solution steps

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

Simplify

e^{x} y d y : e^{x} y^{2} d

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

Treat

y, d

as constants

Take the constant out:

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

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

Apply the common derivative:

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

= y^{2} d e^{x}

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

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\int \frac{1}{x ^{6}} + \frac{3}{x ^{2}} d x

What is (\partial)/(\partial x)(e^x*y*dy) ?
The answer to (\partial)/(\partial x)(e^x*y*dy) is y^2de^x