What is (\partial)/(\partial x)(8xy+2x^4+2y^4) ?

The answer to (\partial)/(\partial x)(8xy+2x^4+2y^4) is 8x^3+8y

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(\partial)/(\partial x)(8xy+2x^4+2y^4)

\frac{\partial}{\partial x} (8 x y + 2 x^{4} + 2 y^{4})

8 x^{3} + 8 y

Solution steps

\frac{\partial}{\partial x} (8 x y + 2 x^{4} + 2 y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x y) + \frac{\partial}{\partial x} (2 x^{4}) + \frac{\partial}{\partial x} (2 y^{4})

\frac{\partial}{\partial x} (8 x y) = 8 y

\frac{\partial}{\partial x} (2 x^{4}) = 8 x^{3}

\frac{\partial}{\partial x} (2 y^{4}) = 0

= 8 y + 8 x^{3} + 0

Simplify

= 8 x^{3} + 8 y

\frac{d}{d x} (sin^{n - 2} (x))

\frac{\partial}{\partial x} (\frac{- cos ( x )}{x})

\frac{0.6 e ^{x}}{cos ( x )}

3^{x}

x \to 1 lim (- 4 x + 6)

What is (\partial)/(\partial x)(8xy+2x^4+2y^4) ?
The answer to (\partial)/(\partial x)(8xy+2x^4+2y^4) is 8x^3+8y