how do i find the derivative of this function??
f(x) = e^2x * cos(4x)
2007-12-14 02:47:14 · 4 answers · asked by Britney 1 in Science & Mathematics ➔ Mathematics
According to the rule for derivatives of products and the chain rule,
f'(x) = (e^(2x)' cos(4x) + e^(2x) (cos(4x))' = 2 e^(2x) cos(4x) + e^(2x) (-sin(4x)) 4 = 2 e^(2x) [cos(4x) - 2 sin(4x)]
2007-12-14 03:15:55 · answer #1 · answered by Steiner 7 · 0⤊ 0⤋
Its equal to the derivative of (e^2x) times cos(4x), plus (e^2x) times the derivative of (cos(4x)). This is called the "chain rule".
2007-12-14 02:51:54 · answer #2 · answered by morningfoxnorth 6 · 0⤊ 0⤋
By the product rule:
If f(x) = g(x)h(x)
f'(x) = g'(x)h(x) + h'(x)g(x)
= 2e^2x cos(4x) - 4 sin(4x) e^2x
= e^2x (2 cos(4x) - 4 sin(4x))
2007-12-14 02:53:17 · answer #3 · answered by mediaptera 4 · 0⤊ 0⤋
2*e^2x * cos (4x) + e^2x * -sin(4x)*4
2007-12-14 02:54:20 · answer #4 · answered by derflori90 2 · 0⤊ 0⤋