i think you mean:

1. f(x) = (1/5)x^4 - (1/5)x^9

and

2. c = -820/q + [3700*e^{(2q+3)/820}]/q

1. f(x) = (1/5)x^4 - (1/5)x^9

=> f'(x) = (4/5)x^3 - (9/5)x^8 ............by the power rule

2. c = -820/q + [3700*e^{(2q+3)/820}]/q

there are two ways you can do this. change /q to q^-1 and use the power rule with the product rule on the second term. or combine the fractions with q as the common denominator and use the quotient rule. i prefer using the power rule with product rule.

=> c = -820q^-1 + 3700*e^{(2q+3)/820}*q^-1

=> c' = 820q^-2 + 3700[(2/820)e^{(2q+3)/820}*q^-1 - e^{(2q+3)/820}*q^-2]

=> c' = 820q^-2 + (370/41)e^{(2q+3)/820}*q^-1 - 3700*e^{(2q+3)/820}*q^-2

=> c' = (820 - 3700*e^{(2q+3)/820})q^-2 + (370/41)e^{(2q+3)/820}*q^-1