Calculus deriveatives

Question

Let f(x)=xsin(x). Find f′′(3.2).

Answer 1

To find f', use the product rule: x'*sin(x) + x(sin(x))' = sin(x) + xcos(x)

To find f'' take the derivative of f' = (sin(x))' + (by the product rule) x'cos(x) + x(cos(x))' = cos(x) + cos(x) -xsin(x) = 2cos(x) - x sin(x)

To find f''(3.2), plug 3.2 in for x to get: 2cos(3.2) - 3.2*sin(3.2) = -1.8098