tentukan turunan dari fungsi f(x)=√x pada nilai x=4. Menggunakan rumus F'(a)= Lim f(a+h)-f(a) / h h→0

Langsung aja y

f(x) = √x
f(x) = x^½

f'(x) = ½x^(½-1)
f'(x) = ½x^-½
f'(x) = ½ / x^½

f'(4) = ½ / 4^½
f'(4) = ½ / 2
f'(4) = ¼

Semoga berguna +_+

f(x) = x^(1/2)
f'(x) = lim(a→0) [f(x+a) - f(x)]/a
= lim(a→0) [(x + a)^(1/2) - x^(1/2)]/a
= lim(a→0) {[(x + a)^(1/2) - x^(1/2)].[(x + a)^(1/2) + x^(1/2)]}/{a.[(x + a)^(1/2) + x^(1/2)]}
= lim(a→0) [(x + a) - x]/a.[(x + a)^(1/2) + x^(1/2)]
= lim(a→0) a/{a.[(x + a)^(1/2) + x^(1/2)]}
= lim(a→0) 1/[(x + a)^(1/2) + x^(1/2)]
= 1/[x^(1/2) + x^(1/2)]
= 1/[2x^(1/2)]
f'(4) = 1/[2.4^(1/2)] = 1/(2.2) = 1/4

semoga membantu! :)