What is (\partial)/(\partial x)(e^x+y+y^2+6) ?

The answer to (\partial)/(\partial x)(e^x+y+y^2+6) is e^x

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(\partial)/(\partial x)(e^x+y+y^2+6)

\frac{\partial}{\partial x} (e^{x} + y + y^{2} + 6)

e^{x}

Solution steps

\frac{\partial}{\partial x} (e^{x} + y + y^{2} + 6)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{x}) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (6)

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

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

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

\frac{\partial}{\partial x} (6) = 0

= e^{x} + 0 + 0 + 0

Simplify

= e^{x}

x \to 0 lim (ln (1 - x))

\int (cos^{4} (x)) (sin (x)) d x

\frac{d}{d x} (5 3 x^{2})

x \to - 6 lim (6 x + 1)

\frac{d ^{2}}{d x ^{2}} (\frac{2 x + 3}{3 x - 1})

What is (\partial)/(\partial x)(e^x+y+y^2+6) ?
The answer to (\partial)/(\partial x)(e^x+y+y^2+6) is e^x