Question

Tentukan turunan dari

f (x) = sinxcosx

f (x) = cosx (x^2-sinx)

f (x) = x^2.secx

f (x) = x^2/tanx

f (x) = cotx / cosecx - 1

f (x) = x^2 / cosx + 1

f (x) = sinx + cos x / sinx - cosx

Answer 1

F(x) = sin x . cos x
f(x) = u . v
u = sin x  --> u' = cos x
v = cos x  --> v' = - sin x
f'(x) = u'.v + u.v'
f'(x) = cos x . cos x + sin x . (- sin x)
      = cos² x - sin² x
      = cos 2x
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f(x) = cos x (x² - sin x)
u = cos x  --> u' = - sin x
v = x² - sin x --> v' = 2x - cos x
f'(x) = u'.v + u.v'
      = - sin x (x² - sin x) + cos x (2x - cos x)
      = - x² . sin x + sin² x + 2x . cos x - cos² x
      = - x² . sin x + 2x . cos x + sin² x - cos² x
      = - x² . sin x + 2x . cos x - cos 2x
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f(x) = x² . sec x
u = x² --> u' = 2x
v = sec x --> v' = sec x . tan x
f'(x) = u'.v + u.v'
      = 2x . sec x + x² . (sec x . tan x)
      = x . sec x (2 + x . tan x)

semoga membantu ya :)