Page 157 - Math Grade 11 (Basic)

PROEUS DARA

2
n. y' = (x )'+(4x)' = 2x+4 , y'(O) = 2x0+4 = 4
y'(-2) = 2(-2)+4 = 4-4 = 0 '1

3 2 2 ?
2. y' = (x )'- (3x )' = 3x - 6x , y'( 1) = 3 x 1--6 x 1 = -3
?
y'(-1) = 3(-It-6(-1) = 9 '1
4 2
?1. y' = (x )' (2x )'+(3x)' (2)' = 4i-4x+3
3
y'(O) = 4x0 -4x0+3 = 3 '1

"" " 1 3 2
y'(O) s~ y'(l) ts y = x· -x '1
3

"
0
- LHmHHli?irul&SHS?i'i:3S : y = f(x) · g(x)
"'
I I
&?iffl~ F(x) = f(x) · g(x)
t?itflS F(x+h)-F(x) = f(x+h)·g(x+h)-f(x)·g(x)

= f(x +h)· g(x +h) g(x +h)· f(x) + g(x +h)· f(x)- f(x) · g(x)

= [f(x +h)- f(x)]g(x +h)+ f(x)[g(x +h)- g(x)]

. F(x+h)-F(x)
y' = F' (X) = 1 lffi --'----:'----'---'-
h->0 h
. j"(x +h)- f(x) . "'-g('-x_+_h;-) -_,g"-'-(-'-x)
= hm ·g(x+h)+ hmf(x)·
h-0 h h-0 h
= f'(x) · g(x) + f(x) · g'(x)
..,
m y = f(x) · g(x) &S"H y' = f'(x) · g(x) + f(x) · g'(x)

0 • 0 ~ "" " "'
ruUTHif:U n. ?irulS"HwH1 y' S~ y'(-1) &SHS?i'i:3S y = x(x-!) '1
u I
~ "" " "' 2 2
2. ?irulS"ltwH~ y' S~ y'(O) &SHS?i'i:3S y = (x -2)(3x +x) '1
1
n. y' = (x)'(x-I)+x(x-1)' = (l)(x-l)+x(l) = 2x-J

y'(-1) = 2(-1) 1 = -3 '1

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