What is (\partial)/(\partial x)(2x^y+8y^x+10) ?

The answer to (\partial)/(\partial x)(2x^y+8y^x+10) is 2yx^{y-1}+8y^xln(y)

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(\partial)/(\partial x)(2x^y+8y^x+10)

\frac{\partial}{\partial x} (2 x^{y} + 8 y^{x} + 10)

2 y x^{y - 1} + 8 y^{x} ln (y)

Solution steps

\frac{\partial}{\partial x} (2 x^{y} + 8 y^{x} + 10)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{y}) + \frac{\partial}{\partial x} (8 y^{x}) + \frac{\partial}{\partial x} (10)

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

\frac{\partial}{\partial x} (8 y^{x}) = 8 y^{x} ln (y)

\frac{\partial}{\partial x} (10) = 0

= 2 y x^{y - 1} + 8 y^{x} ln (y) + 0

Simplify

= 2 y x^{y - 1} + 8 y^{x} ln (y)

What is (\partial)/(\partial x)(2x^y+8y^x+10) ?
The answer to (\partial)/(\partial x)(2x^y+8y^x+10) is 2yx^{y-1}+8y^xln(y)