Respuesta :

Answer

You need to simplify the function first until the exponent turns into a plain x. Step 1 Leave 1/3 alone that is the a value, initial value. You are looking for the base

Step 2 Deal with the parenthesis. Factor 24 and you will get 2 and the cube of 3. 

Step 3 Separate the exponent (2) (x)

Step 4 Now square each term inside the parenthesis

2 squared and cube of 3 square  the 2^2 will be 4, the other expression means  cube of 3 times cube of 3 and that's cube of 9

Step 5 Your base should be (4 cube of 9)

lublana

Answer:

[tex]f'(x)=\frac{4}{3^{\frac{1}{3}}}[/tex]

Step-by-step explanation:

We are given that a function

[tex]f(x)=\frac{1}{3}(\sqrt[3]{24})^2 x[/tex]

We have to find the rate of increase of the given function.

Differentiate w.r.t x

Then, we get

[tex]f'(x)=\frac{1}{3}(\sqrt[3]{24})^2[/tex]

Using formula :  [tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]

[tex]f'(x)=\frac{1}{3}(\sqrt[3]{2\times 2\times 2\times 3})^2[/tex]

[tex]f'(x)=\frac{1}{3}(2)^2(3^{\frac{2}{3}})[/tex]

[tex]f'(x)=\frac{4}{3^{1-\frac{2}{3}}}[/tex]

Using identity:[tex]\frac{a^x}{a^y}=a^{x-y}[/tex]

[tex]f'(x)=\frac{4}{3^{\frac{1}{3}}}[/tex]

Hence, the rate of increase of the function =[tex]f'(x)=\frac{4}{3^{\frac{1}{3}}}[/tex]

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