Question

Diketahui fungsi f dan g dengan f(x).g(x)=x^2-3x untuk setiap bilangan real x. jika g(1)=2, f'(1)=f(1), dan g'(1)=f'(1), nilai g'(1)=...?

Answer 1

F (x) . g (x) = x² - 3x

g (1) = 2
f ' (1) = f (1)
g ' (1) = f ' (1)
g' (1) = ...?

f (x) . g (x) = x² - 3x
f (1) . g (1) = (1)² - 3(1) = 1 - 3 = -2
f (1) . 2 = -2
f (1) = -2 / 2
f (1) = -1

f (x) . g (x)
turunkan

u = f (x)
u' = f ' (x)

v = g (x)
v ' = g ' (x)

u'v + uv' = 2x - 3
f ' (x) . g (x) + f (x) . g ' (x) = 2x - 3
jadikan (x) menjadi (1)
f ' (1) . g (1) + f (x) . g ' (x) = 2(1) - 3

-1 . 2 + (-1) . g' (1) = -1
-2 - g' (1) = -1
- g ' (1) = -1 + 2
- g ' (1) = 1
g ' (1) = -1

Maaf lama kak jawabnya. Pusing dulu tadi, hahaha.