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Calculate the derivative.$$W(y)=6 y^{4}+7 y^{2 / 3}$$

$24 y^{3}+\frac{14}{3 y^{1 / 3}}$

Calculus 1 / AB

Chapter 3

DIFFERENTIATION

Section 2

The Derivative as a Function

Derivatives

Differentiation

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hi. Today we will be solving the following problem. I need derivative off W Why? Which is defined as six times y to the power four plus seven times y to the power of two thirds. Now who saw this problem? Let's review the power rule taking derivatives. That is, if you want to take me during the function and I can sing to find I'm taking the derivative with respect to X pricing ttx off they function x to the power fi he derivative of Except horrify is going to be high times X to the power of I minus one. Now we have a constant before X any value so we can write that out by saying the derivative or ddx of some constant C times X to have heart I and note that X is a variable, while I and Sea air with constant numbers the derivative off. That would be see Time's D D acts according to the derivative with respect to X of X to the party. And this is because the value of seas Constance, who doesn't change with X so you can move outside of the derivative and that would be equal to see times I time's acts to the power ofthe eye minus one. Now we can use these principles to solve for the derivative of w fl y. You know, when my examples I used the variable X But since we're taking the deer made with respect to why the prose was the exact same thing but was just different and it was a different name for the variable. Oh, so look table to fall this stuff over here and start solving court are derivative off w off. Why? Okay, so we have a W for rising to six times why? To par four plus seven times y to the power of two thirds. So the derivative w y, and I conclude an apostrophe here to signify that I'm taking the first derivative is equal to So first, let's take the derivative of six times White have power for core here eating the power will. It would be six times four off. Why? To the power of four minus one Sold three. Now let's take the derivative of seven times. Watch part two thirds. So he dirt of seven times while his heart two thirds his seven times two affairs time to y to the power two thirds minus one. So we just negative one third that we can simplify this further and say six times. Forest twenty four. So we have twenty four. Why? To power three and then seven times two thirds. He's equal to fourteen over three. Why? To the power of negative one third. And that's it. There's preservative, huh? W off. Why, thank you for watching.

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