What is (\partial)/(\partial x)(3x^4y^2+2xy^2-5) ?

The answer to (\partial)/(\partial x)(3x^4y^2+2xy^2-5) is 12x^3y^2+2y^2

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(\partial)/(\partial x)(3x^4y^2+2xy^2-5)

\frac{\partial}{\partial x} (3 x^{4} y^{2} + 2 x y^{2} - 5)

12 x^{3} y^{2} + 2 y^{2}

Solution steps

\frac{\partial}{\partial x} (3 x^{4} y^{2} + 2 x y^{2} - 5)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{4} y^{2}) + \frac{\partial}{\partial x} (2 x y^{2}) - \frac{\partial}{\partial x} (5)

\frac{\partial}{\partial x} (3 x^{4} y^{2}) = 12 y^{2} x^{3}

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

\frac{\partial}{\partial x} (5) = 0

= 12 y^{2} x^{3} + 2 y^{2} - 0

Simplify

= 12 x^{3} y^{2} + 2 y^{2}

(- 1, 4), (- 3, - 2)

\int arctan (4 t) d t

\frac{\partial}{\partial y} (- y)

\frac{ln ( x )}{x ^{6}}

x \to \infty lim (0.99)

What is (\partial)/(\partial x)(3x^4y^2+2xy^2-5) ?
The answer to (\partial)/(\partial x)(3x^4y^2+2xy^2-5) is 12x^3y^2+2y^2