Question

What is the slope of the tangent line of `r=(sin^2theta)/(2theta-thetacos2theta)` at `theta=(pi)/4`?

Answer 1

slope is the derivative value at a given value of `theta`

Explanation:

dr/d`theta`
by quotient rule:
it is
`(2sinthetacostheta(2theta -thetacos2theta) - (sin^2theta)(2 - (cos2theta + theta(-sin2theta)*2)))/(2theta - thetacos2theta)^2`
now placing the value of `theta = pi/4`
you can find slope
hope u find it helpful :)