What is the d/(dy)(4x^2y^3+2) ?

The d/(dy)(4x^2y^3+2) is 12x^2y^2

What is the first d/(dy)(4x^2y^3+2) ?

The first d/(dy)(4x^2y^3+2) is 12x^2y^2

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

12 x^{2} y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d y} (2) = 0

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

Simplify

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

\int \frac{x ^{2}}{( 8 - x ^{3} ) ^{2}} d x

72 t

x \to 0 lim (- x + 3)

\frac{3 x - y}{- x + y}

n = 0 \sum \infty \frac{1}{2 ^{n} + 1}