What is (\partial)/(\partial x)(e^y+x+x^2+4) ?

The answer to (\partial)/(\partial x)(e^y+x+x^2+4) is 2x+1

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(\partial)/(\partial x)(e^y+x+x^2+4)

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 4)

2 x + 1

Solution steps

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 4)

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} (4)

\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} (4) = 0

= 0 + 1 + 2 x + 0

Simplify

= 2 x + 1

x \to 2 - lim ((x - 3)^{2})

\int (3 u + 2)^{3} d u

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\int \frac{7}{y} d y

What is (\partial)/(\partial x)(e^y+x+x^2+4) ?
The answer to (\partial)/(\partial x)(e^y+x+x^2+4) is 2x+1