What is (\partial)/(\partial x)(3y^2+20x^2y^3) ?

The answer to (\partial)/(\partial x)(3y^2+20x^2y^3) is 40y^3x

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(\partial)/(\partial x)(3y^2+20x^2y^3)

\frac{\partial}{\partial x} (3 y^{2} + 20 x^{2} y^{3})

40 y^{3} x

Solution steps

\frac{\partial}{\partial x} (3 y^{2} + 20 x^{2} y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

\frac{\partial}{\partial x} (20 x^{2} y^{3}) = 40 y^{3} x

= 0 + 40 y^{3} x

Simplify

= 40 y^{3} x

cos^{2} (π t)

f^{^{'}} (x) = \frac{9}{2 9 x - 5}

\int 4 x - 3 d x

\int \frac{x + 5}{( x + 3 ) ( x - 2 ) ^{2}} d x

\frac{d y}{d t} - 2 t y = - 12 t^{2} e^{t^{2}}, y (0) = - 1

What is (\partial)/(\partial x)(3y^2+20x^2y^3) ?
The answer to (\partial)/(\partial x)(3y^2+20x^2y^3) is 40y^3x