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

The answer to (\partial)/(\partial x)(5x^4y^2+xy^3+4) is y^3+20x^3y^2

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

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

y^{3} + 20 x^{3} y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{4} y^{2}) = 20 y^{2} x^{3}

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

\frac{\partial}{\partial x} (4) = 0

= 20 y^{2} x^{3} + y^{3} + 0

Simplify

= y^{3} + 20 x^{3} y^{2}

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (e^{x})

\int_{1}^{2} \frac{3}{4 x - x ^{2}} d x

f (x) = x - 4, at x = 13

y^{^{'}} = - \frac{2 x}{y}

x \to 1 lim (∣ e^{x} - 1 ∣)

What is (\partial)/(\partial x)(5x^4y^2+xy^3+4) ?
The answer to (\partial)/(\partial x)(5x^4y^2+xy^3+4) is y^3+20x^3y^2