Question

Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = e^x + 3x + 2

Answer 1

y = e^x + 3x + 2
Differentiating w.r.t. x, we get
`"dy"/"dx"(e^x + 3x + 2)`
= e^x + 3 x 1 + 0
= e^x + 3
The derivative of inverse function of y = f(x) is given by
`"dx"/"dy" = (1)/(("dy"/"dx")`
= `(1)/(e^x + 3)`
At x = 0, `"dx"/"dy"`
= `(1)/(e^x + 3)_(at x = 0)`
= `(1)/(e^0 + 3)`
= `(1)/(1 + 3)`
= `(1)/(4)`.