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

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

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

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

2 x + 8 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 x + 0 + 8 y

Simplify

= 2 x + 8 y

\int \frac{7}{x ln ( x )} d x

\frac{\partial}{\partial x} ((x - 4)^{2} + (y - 4)^{2} - 5)

\int \frac{x}{16 - 9 x ^{4}} d x

\int \frac{3 x ^{2} - 10}{x ^{2} - 4 x + 4} d x

y^{^{''}} - 6 y^{^{'}} + 13 y = 0

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