What is (\partial)/(\partial x)(e^y+x+x^2+9) ?

The answer to (\partial)/(\partial x)(e^y+x+x^2+9) is 2x+1

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(\partial)/(\partial x)(e^y+x+x^2+9)

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 9)

2 x + 1

Solution steps

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 9)

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} (9)

\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} (9) = 0

= 0 + 1 + 2 x + 0

Simplify

= 2 x + 1

\int (\frac{4 x}{y}) d x

\frac{d y}{d x} = x - y

16 - x^{2}, x^{2} - 2

\int 4 - \frac{4}{x ^{2}} d x

x \to 0 lim (\frac{7 sin ( x )}{x})

What is (\partial)/(\partial x)(e^y+x+x^2+9) ?
The answer to (\partial)/(\partial x)(e^y+x+x^2+9) is 2x+1