What is (\partial)/(\partial x)(x(e^y+e^yy)) ?

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

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(\partial)/(\partial x)(x(e^y+e^yy))

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

e^{y} + e^{y} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

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

Simplify

= e^{y} + e^{y} y

\frac{d}{d x} (\frac{csc ( x ) tan ( x )}{cos ( x )})

\int sin^{4} (x) \cdot cos (x) d x

x, x, [0, 2]

f (x) = x^{2} - 6 x + 25, at x = 0

f (x) = x^{4} + 7 e^{x}, (0, 7)

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