Introduction to the study of polar derivative formulas:* In calculus, differentiation is the process of finding the derivative, which means measuring how a function changes with respect to its entrance. The derivative of y with respect to x is given by [(dy)/(dx)].* The polar coordinate is a two-dimensional coordinate system and is defined by x = rcos θ, y = rsin θ. To find the derivative [(dy)/(dx)] of polar coordinates, we can use the following formula.Polar Derivative Formula:Study on Polar Derivative FormulasIn this article, we will see some examples and practice problems that will help you to study the formulas of polar derivatives. Example problems to study on polar derivative formulas: Study on polar derivative formulas with example problem 1: Find the derivative of the function r = 8 + 5sin θStep 1: Given function = 8 + 5sin θStep 2: Differentiate the given function r = 8 + 5sin θ with respect to 'θ' [(dr)/(d theta)] = 5cos θStep 3: Substitute all values ​​into the polar coordinate formula [(dy)/dx] = [ ((dr)/ (d theta) sin theta + r cos theta)/((dr)/(d theta)cos theta - r sin theta)] .= [((5cos theta) sin theta + (8 + 5sin theta ) cos theta)/ ((5cos theta) cos theta - (8 + 5sin theta)sin theta)]= [(5cos theta sin theta + 8cos theta + 5sin theta cos theta)/(5cos^2 theta - 8sin theta - 5sin ^2 theta)] = [(10cos theta sin theta + 8cos theta)/(5cos^2 theta - 8sin theta - 5sin^2...... middle of paper ......ta) cos theta)/ ((5sec^2 theta) cos theta - (5tan theta)sin theta)]= [((5)/(5))] [(sec^2 theta sin theta + tan theta cos theta)/(sec^2 theta cos theta - tan theta theta)]= [(sec^2 theta sin theta + tan theta cos theta)/(sec^2 theta cos theta - tan thetasin theta)]Practical problems to study on polar derivative formulas:1) Find the derivative of the function r = 2 + 7sin θ2) Find the derivative of the function r = -4cos 9θ3) Find the derivative of the function r = - 6tan θSolutions:1) [(14cos theta sin theta + 2cos theta)/ (7cos^2 theta - 2sin theta - 7sin ^2 theta)]2) [(9sin 9theta sin theta - cos 9theta cos theta)/(9sin 9theta cos theta + cos 9theta sin theta)]3) [(sec^2 theta sin theta + tan theta cos theta)/( sec^2 theta cos theta - tan thetasine theta)]