What is (\partial)/(\partial x)(e^y+x+x^2+5) ?

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

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(\partial)/(\partial x)(e^y+x+x^2+5)

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 5)

2 x + 1

Solution steps

\frac{\partial}{\partial x} (e^{y} + x + x^{2} + 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^{2}) + \frac{\partial}{\partial x} (5)

\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} (5) = 0

= 0 + 1 + 2 x + 0

Simplify

= 2 x + 1

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

y = 3 t + 4 t^{3}

\int \frac{x}{( 4 x ^{2} + 3 ) ^{2}} d x

\int cos (2 x) cos (4 x) d x

\frac{d}{d x} (f (h, x) \cdot g (h, x) \cdot h)

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