Question

Find the derivative of the inverse function of the following : y = x cos x

Answer 1

y = x cos x
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(xcosx)`
= `x"d"/"dx"(cosx) + cosx"d"/"dx"(x)`
= x(– sinx) + cosx x 1
= cosx –x sinx
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(cosx - xsinx)`.