Answer
a) $f'(x) = 8x^7 - \frac{3}{2\sqrt{x}}-15x^{-4}$
b) $f'(x) = (2x+1)^{100} ( 1030x^2+10x-1414)$
Work Step by Step
We find:
a) $f'(x) = 8x^7-3 * (\frac{1}{2}) * (x^{-\frac{1}{2}}) + 5 * (-3) * x^{-4} = 8x^7 - \frac{3}{2\sqrt{x}}-15x^{-4}$
b) $f'(x) = 101 (2)(2x+1)^{100}(5x^2-7) + (10x)(2x+1)^{101} = (2x+1)^{100} (202(5x^2-7) + 10x(2x+1)) = (2x+1)^{100} ( 1030x^2+10x-1414)$
