Solved Examples of Applications of DerivativesWell acknowledged with the various applications of derivatives, let us practice some solved examples to understand them with a mathematical approach.Example 1: Find the rate of change of the area of a circle with respect to its radius r when r = 6 cm.Solution:Here we have to find the rate of change of the area of a circle with respect to its radius r when r = 6 cm.As we know, the area of a circle is given by: \(π ⋅ r^2\) where r is the radius of the circle.Let A =\(π ⋅ r^2\)Also, we know that, if y = f(x), then dy/dx denotes the rate of change of y with respect to x.So, by differentiating A with respect to r we get,⇒\(\frac{dA}{dr}=\frac{d}{dr}\left(\pi⋅r^2\right)=2\pi r\)Now we have to find the value of dA/dr at r = 6 cm i.e \(\left[\frac{dA}{dr}\right]_{_{r=6}}\)⇒\(\left[\frac{dA}{dr}\right]_{_{r=6}}=2\pi⋅6=12\pi\text{ cm }\)Hence, the rate of change of the area of a circle with respect to its radius r when r = 6 cm is 12π cm.Learn about...
