Question

Find the derivative using the first principles. ​

Answer 1

`~~~~(d)/(dx) \left( \sqrt[5]{1+x} \right)\\\\\\=(d)/(dx) (1+x)^(\tfrac 15)\\\\\\=\frac 15 \left(1 + x\right)^(\tfrac 15 -1) \cdot (d)/(dx)(1+x)\\\\\\=\frac 15 (1+x)^(-\tfrac 45) \cdot(0+1)\\\\\\=(1)/(5(1+x)^(\tfrac 45))`