What is (\partial)/(\partial y)(x^4+8xy^7) ?

The answer to (\partial)/(\partial y)(x^4+8xy^7) is 56xy^6

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(\partial)/(\partial y)(x^4+8xy^7)

\frac{\partial}{\partial y} (x^{4} + 8 x y^{7})

56 x y^{6}

Solution steps

\frac{\partial}{\partial y} (x^{4} + 8 x y^{7})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4}) + \frac{\partial}{\partial y} (8 x y^{7})

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

\frac{\partial}{\partial y} (8 x y^{7}) = 56 x y^{6}

= 0 + 56 x y^{6}

Simplify

= 56 x y^{6}

\int \frac{ln ∣ x ∣}{x} d x

f (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

x \to 0 lim (\frac{tan ( k x )}{x})

\int z^{3} e^{z} d z

\frac{d}{d x} (arctan (ln (x^{2})))

What is (\partial)/(\partial y)(x^4+8xy^7) ?
The answer to (\partial)/(\partial y)(x^4+8xy^7) is 56xy^6