Y=(6+3X)^2/3 Find the derivative of the function using the chain rule

Mathematics

1 answer:

fomenos4 years ago

5 0

$\bf y=(6+3x)^{\frac{2}{3}}\implies \cfrac{dy}{dx}=\stackrel{chain~rule}{\cfrac{2}{3}(6+3x)^{\frac{2}{3}-1}\cdot (0+3)}
\\\\\\
\cfrac{dy}{dx}=\cfrac{2}{3}(6+3x)^{-\frac{1}{3}}\cdot 3\implies \cfrac{dy}{dx}=2(6+3x)^{-\frac{1}{3}}\implies \cfrac{dy}{dx}=\cfrac{2}{\sqrt[3]{6+3x}}$

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Answer:

The vertex is the point $(-\frac{1}{3},0)$

Step-by-step explanation:

we know that

The general form of an absolute value equation is

$y=a\left|x-h\right|+k$

The variable a tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables h, and k, tell us how far the graph shifts horizontally and vertically

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