Question

Differentiate the function. y=(3x+8) 4 dx dy ​ =

Answer 1

The final answer
`\( y' = 12(3x + 8)^3 \)` represents the derivative of the given function. It incorporates both the power rule and the chain rule, accounting for the composition of functions and the exponentiation of the outer function.

`y'` =
`\[ (dy)/(dx) = 12(3x + 8)^3 \]`

Step-by-step explanation:

Let's differentiate the given function step by step using the chain rule:

Given function:

`\[ y = (3x + 8)^4 \]`

Identify the Inner Function
`\( u \)` :

`\[ u = 3x + 8 \]`

Apply the Power Rule to the Outer Function:

`\[ y' = 4(3x + 8)^3 \]`

Apply the Chain Rule:

`\[ y' = 4 \cdot 3 \cdot (3x + 8)^3 \]`

Simplify:

`\[ y' = 12(3x + 8)^3 \]`

Complete Question:

Differentiate the function. y=(3x+8) 4 ​,
`(dy)/(dx)`= ?