Hi Stu,

Stu:

1. Differentiate (use appropiate notation)
a) y = x⁹
y'=9x⁸

b) f(x)=5x³ - 3x + 6
f'(x)=15x² -3

c) y = 4x^-5
y'=20x⁴ (You could have used dy/dx= but y' is fine as well - But it should have been y' = -20x^-5-1 = ?) Can you finish this please Stu

2. d/dx (-12x)
f"(x) = -12 Not f"(x) You only use " when you differentiate twice.
The best answer would be d/dx (-12x) = -12

3. differentiate
a) y = (2x+3)⁴
y' = 4*(2x+3)³*2 That is correct but you can simplify this answer.

b) f(x) = x² ( 2x+3)⁴
f'= 2x+4*(2x+3)³*2

b) f(x) = x² ( 2x+3)⁴
For this question you need to use the product rule. If y=uv then y'=uv' + vu'
u=x² so u'=2x
v=(2x+3)⁴ so v'=4(2x+3)³*2 = 8(2x+3)³
Now you have to substitute those values into the formula and simplify the answer.
Could you try doing that please Stu?

Thanks,
Melody.