What is the derivative of f(x)=(10-3x)/2• sqrt of (5-x)?
f(x)=(10-3x) / 2√(5-x)
quotient rule:
f'(x) = [(-3)(2√(5-x))-(10-3x)/-√(5-x)] / 4(5-x)
= [-6(5-x)+(10-3x)] / 4(5-x)^(3/2)
= (3x-20) / 4(5-x)^(3/2)
Using product rule:
f(x) = 1/2 (10-3x)(5-x)^(-1/2)
f'(x) = 1/2[(-3)(5-x)^(-1/2) + (10-3x)(-1/2)(5-x)^(-3/2)]
massage that and it will end up the same.