3. What is the geometrical meaning of differentiation? 4. Differentiate the following functions using the first principle. (a) \( y=x^{2}+3 x-4 \) (b) \( y=\frac{3 x-4}{2 x+1} \) (c) \( y=\sqrt{x+3} \) (d) \( y=\frac{1}{\sqrt{3}} \)

Differentiation geometrically represents the slope of the tangent line to a function's graph at any given point. This means that the derivative at a specific point not only tells us how steep the graph is there but also indicates whether the function is increasing or decreasing. If you were to zoom in infinitely close to a point on the curve, the curve would begin to resemble a straight line—that's the tangent line, and its slope is your derivative! Now, let’s dive into differentiation using the first principle, which involves taking the limit of the average rate of change as the interval approaches zero. For the function \( y = x^2 + 3x - 4 \), we find that the derivative is \( 2x + 3 \). For \( y = \frac{3x-4}{2x+1} \), applying the first principle gives us \( \frac{3}{(2x+1)^2} \). When differentiating \( y = \sqrt{x+3} \), we get \( \frac{1}{2\sqrt{x+3}} \). Lastly, since \( y = \frac{1}{\sqrt{3}} \) is a constant function, its derivative is \( 0 \).