What is (\partial)/(\partial x)(e^y+x+x^3+5) ?

The answer to (\partial)/(\partial x)(e^y+x+x^3+5) is 3x^2+1

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(\partial)/(\partial x)(e^y+x+x^3+5)

\frac{\partial}{\partial x} (e^{y} + x + x^{3} + 5)

3 x^{2} + 1

Solution steps

\frac{\partial}{\partial x} (e^{y} + x + x^{3} + 5)

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^{3}) + \frac{\partial}{\partial x} (5)

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

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

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

\frac{\partial}{\partial x} (5) = 0

= 0 + 1 + 3 x^{2} + 0

Simplify

= 3 x^{2} + 1

\int_{- 1}^{1} (t^{3} - 9 t) d t

\frac{2}{x - 6}

y^{^{'}} - 2 x y = x y^{2}

\int 12 sin (x) d x

n \to \infty lim (\frac{1}{2 n})

What is (\partial)/(\partial x)(e^y+x+x^3+5) ?
The answer to (\partial)/(\partial x)(e^y+x+x^3+5) is 3x^2+1