Jawaban:
1. 15x⁴
2. 6x-2
[tex]3. - \frac{2}{x} [/tex]
4. 9x²-4x+3
[tex]5. \: \frac{7}{(x + 1)^{2} }[/tex]
1. f(x) = 3x⁵
f'(x) = 3.5.x⁵⁻¹
= 15x⁴
2. f(x) = 3x² - 2x
f'(x) = 3.2.x²⁻¹- 2
= 6x - 2
3. f(x) = 1/x = x⁻¹
f'(x) = -1.x⁻¹⁻¹
= -2x⁻²
4. f(x) = ( x² + 1 ) ( 3x - 2 )
u = x² + 1 v = 3x - 2
u' = 2.x²⁻¹ v' = 3
= 2x
y' = u' v + u v'
= 2x( 3x - 2 ) + ( x² + 1 ) 3
= 6x² - 4x + 3x² + 3
= 9x² - 4x + 3
5.
[tex]f(x) = \frac{4x + 3}{x + 1} [/tex]
u = 4x + 3 v = x + 1
u' = 4 v' = 1
y' = ( u' v - u v' )/ v²
= [ 4( x + 1 ) - ( 4x + 3 ).1 ]/( x + 1 )²
= ( 4x + 4 - 4x - 3 )/( x + 1 )²
= 1/( x + 1 )²
[answer.2.content]
