Problem Set Problem 86 point) Suppose that f(x)=7x^2/5-8x^6/7 Evaluate each of the followin f'(3)= f'(4)= te: You can earn partial credit on this problem.

To find the derivative of the function $f(x)=7x^{2/5}-8x^{6/7}$, we need to use the power rule for differentiation.<br /><br />The power rule states that if $f(x)=x^n$, then $f'(x)=nx^{n-1}$.<br /><br />Let's differentiate each term of the function separately:<br /><br />1. For the first term, $7x^{2/5}$:<br /> - Using the power rule, we get $f'(x) = \frac{2}{5} \cdot 7x^{2/5 - 1} = \frac{14}{5}x^{-3/5}$.<br /><br />2. For the second term, $-8x^{6/7}$:<br /> - Using the power rule, we get $f'(x) = \frac{6}{7} \cdot (-8)x^{6/7 - 1} = -\frac{48}{7}x^{-1/7}$.<br /><br />Now, we can evaluate the derivatives at the given points:<br /><br />1. $f'(3)$:<br /> - Substituting $x=3$ into the derivative, we get $f'(3) = \frac{14}{5} \cdot 3^{-3/5} - \frac{48}{7} \cdot 3^{-1/7}$.<br /><br />2. $f'(4)$:<br /> - Substituting $x=4$ into the derivative, we get $f'(4) = \frac{14}{5} \cdot 4^{-3/5} - \frac{48}{7} \cdot 4^{-1/7}$.<br /><br />Therefore, the answers are:<br />$f'(3) = \frac{14}{5} \cdot 3^{-3/5} - \frac{48}{7} \cdot 3^{-1/7}$<br />$f'(4) = \frac{14}{5} \cdot 4^{-3/5} - \frac{48}{7} \cdot 4^{-1/7}$