find the derivative of the function.

f(x) = − 1/7(x^-7-x^14)

Y = -1/7(X^-7 -X^14).

Y = (-1/7)X^-7 + (1/7)X^14,
Multiply the coefficient of X (1/7) by
the exponent and subtract 1 from the exponent:

dy/dx = 1X^-8 + 2X^13,
dy/dx = 1/X^8 + 2X^13.