1. The problem is to understand the basic concept of differentiation in calculus. 2. Differentiation is the process of finding the derivative of a function, which represents the rate of change or slope of the function at any point. 3. The derivative of a function $f(x)$ is denoted as $f'(x)$ or $\frac{df}{dx}$. 4. The basic formula for the derivative of a power function $f(x) = x^n$ is: $$f'(x) = nx^{n-1}$$ 5. Important rules include: - Constant Rule: The derivative of a constant is 0. - Sum Rule: The derivative of a sum is the sum of the derivatives. - Product Rule: $\frac{d}{dx}[uv] = u'v + uv'$. - Quotient Rule: $\frac{d}{dx}\left[\frac{u}{v}\right] = \frac{u'v - uv'}{v^2}$. - Chain Rule: $\frac{d}{dx}f(g(x)) = f'(g(x)) \cdot g'(x)$. 6. Example: Find the derivative of $f(x) = 3x^4 - 5x^2 + 6$. 7. Apply the power rule to each term: $$f'(x) = 3 \cdot 4x^{4-1} - 5 \cdot 2x^{2-1} + 0$$ 8. Simplify: $$f'(x) = 12x^3 - 10x$$ 9. This derivative tells us the slope of the function $f(x)$ at any value of $x$. This concludes the basic lesson in differentiation.