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Given, y=(ax+b)^(2) , evaluate (dy)/(dx...

Given, `y=(ax+b)^(2)` , evaluate ` (dy)/(dx)`.

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To find \(\frac{dy}{dx}\) for the given function \(y = (ax + b)^2\), we can use two methods: the chain rule or by expanding the expression and then differentiating. Let's go through both methods step by step. ### Method 1: Using the Chain Rule 1. **Identify the inner function and the outer function:** - Inner function: \(u = ax + b\) - Outer function: \(y = u^2\) ...
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Knowledge Check

  • If y = ((ax + b)/(cx + d)), "then" 2 (dy)/(dx).(d^(3) y)/(dx^(3)) is equal to

    A
    `((d^(2) y)/(dx^(2)))^(2) `
    B
    `3(d^(2) y)/(dx^(2))`
    C
    `3((d^(2) y)/(dx^(2)))^(2)`
    D
    ` 3 (d^(2) x)/(dy^(2))`

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