Explications étape par étape :
f(x) = 1 - 2x / 4x + 3
a. f'(x) = -2 ( 4x + 3 ) - [ ( -2x + 1 ) * 4 ] / ( 4x + 3 )²
⇔ f'(x) = -8x - 6 - ( -8x + 4 ) ) / ( 4x + 3 )²
⇔ f'(x) = -8x - 6 + 8x - 4 / ( 4x + 3 )²
⇔ f'(x) = -10 / ( 4x + 3 )²
b. f'(1) = -10 / ( 4*1 + 3 )²
⇔ f'(1) = -10/49
c. f(1) = ( 1 - 2*1 ) / ( 4*1 + 3)
⇔ f(1) = -1/7
y = f'(1) . ( x - 1 ) + f(1)
y = -10/49 . ( x - 1 ) - 1/7
⇔ y = -10/49x + 10/49 - 1/7
⇔ y = -10/49x + 3/49
