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

The answer to (\partial)/(\partial y)(x^y+y) is x^yln(x)+1

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(\partial)/(\partial y)(x^y+y)

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

x^{y} ln (x) + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{y}) = x^{y} ln (x)

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

= x^{y} ln (x) + 1

x \to 3 lim (\frac{1}{x + 3})

f (x) = 4 x^{10} e^{x}

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

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

\frac{x ^{3}}{e ^{\frac{1}{x}}}

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