G'(x) = x^9,7+x^7,9/ x^8,8

To find the derivative \( g'(x) = \frac{x^{9.7} + x^{7.9}}{x^{8.8}} \), we can simplify this expression. 1. Split the expression into separate fractions: \[ g'(x) = \frac{x^{9.7}}{x^{8.8}} + \frac{x^{7.9}}{x^{8.8}} \] 2. Use the property of exponents \( \frac{x^a}{x^b} = x^{a-b} \): \[ g'(x) = x^{9.7 - 8.8} + x^{7.9 - 8.8} \] 3. Simplify the exponents: \[ g'(x) = x^{0.9} + x^{-0.9} \] Therefore, the simplified form of \( g'(x) \) is: \[ g'(x) = x^{0.9} + \frac{1}{x^{0.9}} \] This expression can be further analyzed for specific values or used in further calculus operations if needed!