Question

Find the derivative of the inverse function of the following : y = x ·7^x 

Answer 1

y = x·7^x 

Differentiating w.r.t. x, we get

`"dy"/"dx" = "d"/"dx"(x.7^x)`

= `x"d"/"dx"(7^x) + 7^x"d"/"dx"(x)`

= x·7^x log7 + 7^x × 1

= 7x (x log7 + 1)

The derivative of inverse function of y = f(x) is given by

`"dx"/"dy" = (1)/(("dy"/"dx")`

= `(1)/(7^x(xlog7 + 1)`