What is (\partial)/(\partial y)(4x^3+4xy-1) ?

The answer to (\partial)/(\partial y)(4x^3+4xy-1) is 4x

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(\partial)/(\partial y)(4x^3+4xy-1)

\frac{\partial}{\partial y} (4 x^{3} + 4 x y - 1)

4 x

Solution steps

\frac{\partial}{\partial y} (4 x^{3} + 4 x y - 1)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (4 x^{3}) + \frac{\partial}{\partial y} (4 x y) - \frac{\partial}{\partial y} (1)

\frac{\partial}{\partial y} (4 x^{3}) = 0

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

\frac{\partial}{\partial y} (1) = 0

= 0 + 4 x - 0

Simplify

= 4 x

\frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )}

\frac{d}{d θ} (\frac{5}{2 cos ( θ ) + 7 sin ( θ )})

\frac{d y}{d x} = \frac{( x + 1 )}{y}

\frac{\partial}{\partial y} (x y e^{- 5 y})

\frac{d}{d x} (\frac{16}{x ^{3}})

What is (\partial)/(\partial y)(4x^3+4xy-1) ?
The answer to (\partial)/(\partial y)(4x^3+4xy-1) is 4x