If h(2) = 4 and h'(2) = −5, find (d/dx)(h(x)/x) l x=2

Answer 1

Use the Product Rule: d/dx[h(x)/x] = (d/dx)[h(x)*(1/x)]

= (dh(x)/dx)*(1/x) + h(x)*(d/dx)(1/x)

= (1/x)(dh(x)/dx) - (1/x^2)(h(x))

So evaluating this at x=2, we have (1/2)(-5) - (1/4)(4) = (-5/2) - 1 = -7/2

Answer 2

derivative of a quotient is the quotient of the derivatives of numerator over denominator

derivative of h(x)/x = h'(x)/x' =h'(x) /1 = h'(x)

h'(2) = -5, so

derivative of h(x)/x also = -5 when x=2