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

The answer to (\partial)/(\partial x)(2x^3y^3+3x+4y) is 6x^2y^3+3

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 6 y^{3} x^{2} + 3 + 0

Simplify

= 6 x^{2} y^{3} + 3

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

f (x) = 4 x^{3} - 42 x^{2} + 146 x + 48

\frac{d}{d t} (4 sin (2 t))

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

What is (\partial)/(\partial x)(2x^3y^3+3x+4y) ?
The answer to (\partial)/(\partial x)(2x^3y^3+3x+4y) is 6x^2y^3+3