What is (\partial)/(\partial x)(12x^2y^5+x^2y^2) ?

The answer to (\partial)/(\partial x)(12x^2y^5+x^2y^2) is 24y^5x+2y^2x

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(\partial)/(\partial x)(12x^2y^5+x^2y^2)

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

24 y^{5} x + 2 y^{2} x

Solution steps

\frac{\partial}{\partial x} (12 x^{2} y^{5} + x^{2} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (12 x^{2} y^{5}) = 24 y^{5} x

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

= 24 y^{5} x + 2 y^{2} x

x \to 0 lim (x^{4} f (x))

\int \frac{1}{x ^{2}} (1 + \frac{1}{x})^{\frac{1}{2}} d x

2 y (x + 1) d y = x d x

\frac{1}{x ^{2}}, at 4

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

What is (\partial)/(\partial x)(12x^2y^5+x^2y^2) ?
The answer to (\partial)/(\partial x)(12x^2y^5+x^2y^2) is 24y^5x+2y^2x