Find (d^2y)/(dx^2)
y=9x-8
Please explain because I just started this:(

Question

Find (d^2y)/(dx^2)
y=9x-8
Please explain because I just started this:(

campbell_st · Answer

can you find the 1st derivative..?

what is it?

lukecrayonz · Answer

9

lukecrayonz · Answer

@campbell_st

campbell_st · Answer

ok... so you need to differentiate the 1st derivative to get the 2nd derivative.. 


what happens when you differentiate a constant..?

lukecrayonz · Answer

I understand to find the deriv of the deriv, but is my final answer going to be 9?

lukecrayonz · Answer

0 i meant zero for the last word

campbell_st · Answer

nope... 

the power rule is 

$$y = x^n... y' = nx^{n-1}$$

so think of it as 

$$y' = 9x^0$$

use the power rule.. 

$$y'' = 0 \times 9x^{0-1}$$

and zero times anything is zero...

lukecrayonz · Answer

I had a typo :P I meant zero. But thank you. I didn't know it was simply finding the deriv of the deriv. So for fourth deriv, it's just the deriv of the deriv of the deriv of the deriv?

campbell_st · Answer

thats ok... just remember the derivative of a constant is zero.

thats correct... but you would normally only be asked to find the 1st and 2nd derivatives... as they are critical in curve sketching and rates of change

lukecrayonz · Answer

@campbell_st question :)
f(x)=(x^2+8)^8
f''(x)

campbell_st · Answer

ok... you need the chain rule for the 1st derivative

then the 2nd derivative will need the product rule and chain rule... 

any thoughts on the 1st derivative..

lukecrayonz · Answer

So I take (x^2+8)^8
g(x)=x^2+8
k=8
8(x^2+8)^7*2x

campbell_st · Answer

thats correct... tidy it up a bit and you get

dy/dx = 16x(x^2 + 8)^7

now you need to product and chain rules to get the 2nd derivative

lukecrayonz · Answer

Can you help me with that part? I am horrible at product rule.

lukecrayonz · Answer

Can I just distribute 16x through the parentheses, and get (16x^3+128x)^7 then do chain rule?

campbell_st · Answer

nope... doesn't work like that... because you have 7 lots of (x^2 + 8)

so you would need to do it 7 times and then distribute to get a degree 21 polynomial

lukecrayonz · Answer

So wait, my f(x) is 16x and my g(x) is (x^2+8)^7?

lukecrayonz · Answer

I've only done quotient rules of fractions

campbell_st · Answer

thats correct... 

the product rule is 

y' = f(x) * g'(x) + f'(x)*g(x)

lukecrayonz · Answer

I made a new question, i'll tag you.

campbell_st · Answer

there are plenty of people who can help... no need to tag me