What is (\partial)/(\partial x)(6x^2y^2+5x+8y^3) ?

The answer to (\partial)/(\partial x)(6x^2y^2+5x+8y^3) is 12xy^2+5

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(\partial)/(\partial x)(6x^2y^2+5x+8y^3)

\frac{\partial}{\partial x} (6 x^{2} y^{2} + 5 x + 8 y^{3})

12 x y^{2} + 5

Solution steps

\frac{\partial}{\partial x} (6 x^{2} y^{2} + 5 x + 8 y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{2} y^{2}) + \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (8 y^{3})

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

\frac{\partial}{\partial x} (5 x) = 5

\frac{\partial}{\partial x} (8 y^{3}) = 0

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

Simplify

= 12 x y^{2} + 5

\int \frac{6 x ^{3} - 5}{x} d x

x \to 1 lim (\frac{x ^{15} - 1}{x ^{5} - 1})

(\frac{1}{1 - cos ( x )})^{^{'}}

(\frac{1}{x ^{2} + 1})^{^{'}}

What is (\partial)/(\partial x)(6x^2y^2+5x+8y^3) ?
The answer to (\partial)/(\partial x)(6x^2y^2+5x+8y^3) is 12xy^2+5