If f(x)=4tanx/x
Find f'(x)
2007-10-04 07:41:03 · 5 answers · asked by Rachel 1 in Science & Mathematics ➔ Mathematics
xy = 4tanx
xy' + y = 4sec^2 x
y' = 4*[sec^2 x - tanx / x] / x
2007-10-04 07:47:43 · answer #1 · answered by Dr D 7 · 1⤊ 0⤋
Use the product rule. First expand f(x)
4*[1/x][sinx][1/cosx]. Differentiating
-4/x^2[sinx][1/cosx] +4/x[cosx][1/cosx] +4/x[sinx][sinx/cos^2x]= -4tanx/x^2 +4/x + 4tan^2(x)/x
2007-10-04 14:52:55 · answer #2 · answered by oldschool 7 · 0⤊ 0⤋
Use quotient rule
f '(x) = [x(4sec^2(x) -4tanx]/x^2
= 4(xsec^2(x) -tan(x))/x^2
2007-10-04 14:52:05 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
f(x) = 4 tanx/x
let u = 4tanx
du = 4 sec^2 x
v = x
dv = 1
d(u/v) = vdu - udv/v^2
= 4 x sec^2x - 4tanx /x^2
= 4 (x sec^2x - tan x)/x^2
2007-10-04 14:50:40 · answer #4 · answered by mohanrao d 7 · 0⤊ 1⤋
-4 * [sin(x)*cos(x)-x]
-----------------------
(x^2)*[(cos(x)]^2
2007-10-04 14:51:52 · answer #5 · answered by kirk0791 2 · 0⤊ 0⤋