What is (\partial)/(\partial y)(x^5+xy^7+4) ?

The answer to (\partial)/(\partial y)(x^5+xy^7+4) is 7xy^6

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(\partial)/(\partial y)(x^5+xy^7+4)

\frac{\partial}{\partial y} (x^{5} + x y^{7} + 4)

7 x y^{6}

Solution steps

\frac{\partial}{\partial y} (x^{5} + x y^{7} + 4)

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^{7}) + \frac{\partial}{\partial y} (4)

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

\frac{\partial}{\partial y} (x y^{7}) = 7 x y^{6}

\frac{\partial}{\partial y} (4) = 0

= 0 + 7 x y^{6} + 0

Simplify

= 7 x y^{6}

y^{^{'}} = \frac{( 3 y ^{2} - x ^{2} )}{2 x y}

\frac{d}{d x} (2 x lo g_{6} (x))

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\frac{d}{d y} (y^{4})

\int \frac{3 x ^{3} + 2}{x ^{2} x ^{2} - 4} d x

What is (\partial)/(\partial y)(x^5+xy^7+4) ?
The answer to (\partial)/(\partial y)(x^5+xy^7+4) is 7xy^6