Math 3 (9.10) Jared's Question

Calc test #1; --Jlichtarge

if f(x) = (x^2 - 6x) / (x^3 + 4x^2), what is f'(x)

Answer:

for f(x) = g(x) / h(x) , f'(x) = [ g'(x) h(x) - g(x) h'(x) ] / h(x)^2

thus for g(x) = (x^2 - 6x) and h(x) = (x^3 + 4x^2) , meaning g'(x) = 2x - 6 and h'(x) = 3x^2 + 8x

f'(x) = [ (2x - 6)(x^3 + 4x^2) - (x^2 - 6x)(3x^2 + 8x) ] / [ (x^3 + 4x^2)^2 ]

(do alot of algebra in between)

f'(x) = [-x^4 - 8x^3 - 72x^2] / [x^6 + 8x^5 + 16x^4]