Derivative of

Question

e^tsin(t) -2?

Answer 1

The expression e^{t sin(t)} - 2

Differentiating with respect to t.

Apply chain rule in derivatives.

Recall the formulae : d/dx(e^x) = e^x

d/dx(uv) = uv' + vu'

d/dx(constant) = 0

In this case u = t, v = sin(t)

u' = 1, v' = cos(t)

d/dx[e^{t sin(t)} - 2] = e^{t sin(t)}  d/dx[ t sin(t)]

d/dx[e^{t sin(t)} - 2] = e^{t sin(t)}  [ t cos(t) + sin(t)].