What is (\partial)/(\partial y)(x^5+xy^8+6) ?

The answer to (\partial)/(\partial y)(x^5+xy^8+6) is 8xy^7

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(\partial)/(\partial y)(x^5+xy^8+6)

\frac{\partial}{\partial y} (x^{5} + x y^{8} + 6)

8 x y^{7}

Solution steps

\frac{\partial}{\partial y} (x^{5} + x y^{8} + 6)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{5}) + \frac{\partial}{\partial y} (x y^{8}) + \frac{\partial}{\partial y} (6)

\frac{\partial}{\partial y} (x^{5}) = 0

\frac{\partial}{\partial y} (x y^{8}) = 8 x y^{7}

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

= 0 + 8 x y^{7} + 0

Simplify

= 8 x y^{7}

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

\int \frac{1}{25 + 3 x ^{2}} d x

\int \frac{1}{x ^{2} 16 x ^{2} - 9} d x

\frac{\partial}{\partial x} (1 + x)

\frac{d v}{d x} = - 2 v - 32

What is (\partial)/(\partial y)(x^5+xy^8+6) ?
The answer to (\partial)/(\partial y)(x^5+xy^8+6) is 8xy^7