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

The answer to (\partial)/(\partial x)((y)(x^4+y^4)) is 4yx^3

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(\partial)/(\partial x)((y)(x^4+y^4))

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

4 y x^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= y (4 x^{3} + 0)

Simplify

= 4 y x^{3}

(2 + j + k) (1 - 2 + 2) (3 - 4 = 2 k)

\frac{3 x ^{2} - 7 x - 12}{( x + 4 ) ( x - 4 ) ^{2}}

3 sin (2 (π - θ))

\frac{( e ^{- s} )}{s ( s + 1 )}

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

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