How to find the Cartesian slope of the tangent line to a polar curve r(φ) at any given point by using polar derivative?

How to solve it by using the polar derivative formula? Polar derivative formula is shown below.

dx/dy = (r'(φ) *sin⁡φ + r(φ) *cos⁡φ) / (r' (φ) *cos⁡φ - r(φ) *sin⁡φ )

Example of question

Find the slope of tangent at φ = pi/4

r=5(cos(φ)+1)

Answer 1

[madhan ravi]

Define the formula using syms and then apply diff() for function r and use subs() to plug in the function r and dotr in the main function and plug in phi value using subs() again.

[Muhammad Faiz Aiman Bin Mansor]

Thank you sir for your reply