Penjelasan dengan langkah-langkah:

5. f (x) = 5x - 4

f (x+h) = 5 (x+h) - 4

= 5x + 5h - 4

f'(x) = limit f (x+h) - f (x)

h→0 __________

h

f'(x) = limit 5x + 5h - 4 - (5x - 4)

h→0 ________________

h

f'(x) = limit 5h

h→0 ____

h

f'(x) = limit 5h = 0

h→0

8. f (x) = x² + 3x + 4

f (x+h) = (x+h)² + 3 (x+h) + 4

= x² + 2xh + h² + 3x + 3h + 4

= x² + 2xh + 3x + h² + 3h + 4

f' (x) = limit f (x+h) - f (x)

h→0 __________

h

=limit x² + 2xh + 3x + h² + 3h + 4 - x² + 3x + 4

h→0 _____________________________

h

= limit 2xh + h² + 3h

h→0 __________

h

= limit h (2x + h² + 3h)

h→0 __________

h

= limit 2x + h² + 3h, substitusikan nilai h=0

h→0

= 2x + 0 + 0

jadi f' (x) = 2x

10. f (x) = 2x³

f (x+h) = 2 ( x+h ) ³

= 2 ( x³ + 3x²h + 3xh² + h³ )

= 2x³ + 6x²h + 6xh² + 2h³

f' (x) = limit f (x+h) - f (x)

h→0 __________

h

= limit 2x³ + 6x²h + 6xh² + 2h³ - 2x³

h→0 ______________________

h

= limit 6x²h + 6xh² + 2h³

h→0 ______________

h

= limit h (6x² + 6xh² + 2h³

h→0 ______________

h

= limit 6x² + 6xh² + 2h³

h→0

= 6x² + 6x(0)² + 2(0)³

= 6x²

jadi f' (x) = 6x²