What is (\partial)/(\partial y)(9x^y+2y^x+11) ?

The answer to (\partial)/(\partial y)(9x^y+2y^x+11) is 2xy^{x-1}+9x^yln(x)

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(\partial)/(\partial y)(9x^y+2y^x+11)

\frac{\partial}{\partial y} (9 x^{y} + 2 y^{x} + 11)

2 x y^{x - 1} + 9 x^{y} ln (x)

Solution steps

\frac{\partial}{\partial y} (9 x^{y} + 2 y^{x} + 11)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (9 x^{y}) + \frac{\partial}{\partial y} (2 y^{x}) + \frac{\partial}{\partial y} (11)

\frac{\partial}{\partial y} (9 x^{y}) = 9 x^{y} ln (x)

\frac{\partial}{\partial y} (2 y^{x}) = 2 x y^{x - 1}

\frac{\partial}{\partial y} (11) = 0

= 9 x^{y} ln (x) + 2 x y^{x - 1} + 0

Simplify

= 2 x y^{x - 1} + 9 x^{y} ln (x)

What is (\partial)/(\partial y)(9x^y+2y^x+11) ?
The answer to (\partial)/(\partial y)(9x^y+2y^x+11) is 2xy^{x-1}+9x^yln(x)