What is (\partial)/(\partial x)(y^8+2x^6+2xy) ?

The answer to (\partial)/(\partial x)(y^8+2x^6+2xy) is 2y+12x^5

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(\partial)/(\partial x)(y^8+2x^6+2xy)

\frac{\partial}{\partial x} (y^{8} + 2 x^{6} + 2 x y)

2 y + 12 x^{5}

Solution steps

\frac{\partial}{\partial x} (y^{8} + 2 x^{6} + 2 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y^{8}) + \frac{\partial}{\partial x} (2 x^{6}) + \frac{\partial}{\partial x} (2 x y)

\frac{\partial}{\partial x} (y^{8}) = 0

\frac{\partial}{\partial x} (2 x^{6}) = 12 x^{5}

\frac{\partial}{\partial x} (2 x y) = 2 y

= 0 + 12 x^{5} + 2 y

Simplify

= 2 y + 12 x^{5}

f (x) = 2 x^{3} - 5 x^{2} + 3 x - 7

3 + 5 cos (3 t)

x \to 6 lim (ln (7 - x))

\frac{\partial}{\partial x} (e^{x} tan (y))

x^{3} - 5 x^{2}

What is (\partial)/(\partial x)(y^8+2x^6+2xy) ?
The answer to (\partial)/(\partial x)(y^8+2x^6+2xy) is 2y+12x^5