Subjects calculus

Basic Derivative F468D9

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1. **Stating the problem:** You asked for help with Calculus, but no specific problem was given. 2. **General approach:** Calculus involves concepts like limits, derivatives, integrals, and their applications. 3. **Example problem:** Let's solve a basic derivative problem: Find the derivative of the function $$f(x) = x^2 + 3x + 5$$. 4. **Formula used:** The derivative of $$x^n$$ is $$nx^{n-1}$$, and the derivative of a sum is the sum of derivatives. 5. **Step-by-step solution:** $$f(x) = x^2 + 3x + 5$$ $$f'(x) = \frac{d}{dx}(x^2) + \frac{d}{dx}(3x) + \frac{d}{dx}(5)$$ $$= 2x + 3 + 0$$ 6. **Final answer:** $$f'(x) = 2x + 3$$ This derivative tells us the rate of change of the function at any point $$x$$.