Question

Calculate the first, second and third derivatives of
y = (^^7sqrtx) or x^(1/7)

Answer 1

It's just the power rule:
If \[f(x) = ax^n\]then \[f'(x) = nax^{n-1}\]So...
\[f(x) = x^{1/7} \]\[f'(x) = \frac{1}{7}x^{-6/7}\]\[f''(x) = ]\left(-\frac{6}{7} \right)\frac{1}{7}x^{-13/7} = -\frac{6}{49}x^{-13/7}\]\[f'''(x) = \left(-\frac{13}{7} \right) \frac{-6}{49}x^{-20/7} = \frac{78}{343}x^{-20/7}\]

Answer 2

thanks!