What is (\partial)/(\partial x)(x^{10}+xy^{11}+9) ?

The answer to (\partial)/(\partial x)(x^{10}+xy^{11}+9) is 10x^9+y^{11}

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(\partial)/(\partial x)(x^{10}+xy^{11}+9)

\frac{\partial}{\partial x} (x^{10} + x y^{11} + 9)

10 x^{9} + y^{11}

Solution steps

\frac{\partial}{\partial x} (x^{10} + x y^{11} + 9)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{10}) + \frac{\partial}{\partial x} (x y^{11}) + \frac{\partial}{\partial x} (9)

\frac{\partial}{\partial x} (x^{10}) = 10 x^{9}

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

\frac{\partial}{\partial x} (9) = 0

= 10 x^{9} + y^{11} + 0

Simplify

= 10 x^{9} + y^{11}

What is (\partial)/(\partial x)(x^{10}+xy^{11}+9) ?
The answer to (\partial)/(\partial x)(x^{10}+xy^{11}+9) is 10x^9+y^{11}