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

The answer to (\partial)/(\partial x)(e^y+x+x^2+2) is 2x+1

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

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

2 x + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial x} (2) = 0

= 0 + 1 + 2 x + 0

Simplify

= 2 x + 1

\frac{d y}{- y ln ( \frac{y}{k} )} = c d x

\frac{d y}{d x} + 3 y = 30

y^{^{''}} + 9 y = - 6 tan (3 x)

\frac{d}{d x} ((2) (e^{3 x}))

\int_{0}^{1} t^{2} cos (nπ t) d t

What is (\partial)/(\partial x)(e^y+x+x^2+2) ?
The answer to (\partial)/(\partial x)(e^y+x+x^2+2) is 2x+1