Question

How do you use the Product Rule to find the derivative of `f(x)=cot(x)cos(x)`?

Answer 1

`-cosx-cotxcosecx`

Explanation:

let `u(x)= cotx` `v(x)=cosx` `,f(x)=u(x)v(x)`
according to product rule`d(uv)/dx=udv/dx+vdu/dx`
#d(cotxcossx)/dx=cotx(dcosx/dx)+cosx(d/dx(cotx)) =cotx(-sinx)+cosx(-cosec^2x)=-cosx-cotxcosecx#