What is (\partial)/(\partial x)(2x+3e^y+xy) ?

The answer to (\partial)/(\partial x)(2x+3e^y+xy) is y+2

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(\partial)/(\partial x)(2x+3e^y+xy)

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

y + 2

Solution steps

\frac{\partial}{\partial x} (2 x + 3 e^{y} + x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (3 e^{y}) + \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (3 e^{y}) = 0

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

= 2 + 0 + y

Simplify

= y + 2

\frac{10 s}{( s + 1 ) ( s + 6 )}

\frac{d}{d x} \frac{4 ( y - x \frac{d y}{d x} )}{y ^{2}}

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

\int \frac{6 x + 5}{e ^{x}} d x

y = ln (1 - x^{2})

What is (\partial)/(\partial x)(2x+3e^y+xy) ?
The answer to (\partial)/(\partial x)(2x+3e^y+xy) is y+2