Question

Find the derivative of 7^x w.r.t.x⁷

Answer 1

Let u = 7^x and v = x⁷,

Then we have to find `(du)/(dv)`

∴ `(du)/(dv) = ((du)/(dx))/((dv)/(dx))`   ...(I)

Now, u = 7^x

Differentiate w.r.t.x

`(du)/(dx) = d/(dx)(7^x)` = 7^xlog7  ...(II)

And, v = x⁷

Differentiate w.r.t.x

`(dv)/(dx) = d/(dx)(x^7)` = 7x⁶   ...(III)

Substituting (II) and (III) in (I) we get,

∴ `(du)/(dv) = (7^xlog7)/(7x^6)`