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Question
Find the derivative of the inverse function of the following : y = x ·7x
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Solution
y = x·7x
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·7x log7 + 7x × 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)`
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