Procedure

Find the derivative of the function. f(t) = 4t sin(nt) Step 1 We note that the given function f(t) = 4t sin(nt) is the product of two differentiable functions of the form f(t) = g(t)h(t) where g(t) = 4t and h(t) = sin(nt). However, before we can apply the product rule we must first find h'(t). Doing so requires the use of the chain rule because h(t) = sin(xt) is a composite function with u = nt and h(u) = sin(u). Furthermore, we recall that, in general, if y = sin(v), where u is a differentiable function of t, then, by the chain rule, we have the following. dy = dy du = cos(u) du dt du dt dt So, we first find du dt U = nt du = dt