Differentiate y = x3 from first principles.

May 10, 2026Mathematics

ScanSolve AI Answer

May 10, 2026

Answer

\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$

Morning IT — let's get this done.

To differentiate a function $f(x)$ from first principles, we use the definition of the derivative: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

i) $y = x^3$ Step 1: Identify $f(x)$ and $f(x+h)$ . $f(x) = x^3$ $f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3$ Step 2: Calculate the difference $f(x+h) - f(x)$ .

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Morning IT — let's get this done. To differentiate a function f(x) from first principles, we use the definition of the derivative: f'(x) = _h 0 (f(x+h) - f(x))/(h) i) y = x^3 Step 1: Identify f(x) and f(x+h).

Asked on May 10, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 10, 2026

Morning IT — let's get this done. To differentiate a function f(x) from first principles, we use the definition of the derivative: f'(x) = _h 0 (f(x+h) - f(x))/(h) i) y = x^3 Step 1: Identify f(x) and f(x+h). f(x) = x^3 f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3 Step 2: Calculate the difference f(x+h) - f(x). f(x+h) -