What is (\partial)/(\partial y)((z)(7x+8y^2)) ?

The answer to (\partial)/(\partial y)((z)(7x+8y^2)) is 16zy

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(\partial)/(\partial y)((z)(7x+8y^2))

\frac{\partial}{\partial y} ((z) (7 x + 8 y^{2}))

16 zy

Solution steps

\frac{\partial}{\partial y} ((z) (7 x + 8 y^{2}))

Treat

z, x

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial y} (7 x + 8 y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial y} (7 x) + \frac{\partial}{\partial y} (8 y^{2}))

\frac{\partial}{\partial y} (7 x) = 0

\frac{\partial}{\partial y} (8 y^{2}) = 16 y

= z (0 + 16 y)

Simplify

= 16 zy

- \frac{6}{( x - 3 ) ^{2}}

(x - 2 + 8 i) (x - 2 - 8 i) (x - 4) (x - 1) (2 x - 1)

(p e^{b x} + n e^{- b x}) cos (a x)

\frac{1}{120 ( x - 1 ) ( x - 2 ) ( x - 3 ) ( x - 4 )}

(5 - x + 17) \cdot (5 + x + 17)

What is (\partial)/(\partial y)((z)(7x+8y^2)) ?
The answer to (\partial)/(\partial y)((z)(7x+8y^2)) is 16zy