Solution 1
y = log base 3 (8x^7 + x)
u = 8 x^7 + x
dy/dx = 56 x^6 + 1
= (56 x^6 + 1) / (8 x^7 + x) log base 3 e
Solution 2
P = ln 6s^3 + s
u = 6s^3
dy/dx = 18 s^2
= (18s^2)/(6s^3) + 1
Solution 2
P = ln 6s^3 + s
u = 6s^3 + s
dy/dx = 18 s^2 + 1
= (18s^2 + 1)/(6s^3 + s)
Solution 3
y = 15 x^3 + 7/(2x^3) - x
y = 15x3 + 7 *2 x^-3 - x
dy/dx = 45 x^2 + 42 x^-4 - 1
Solution 3
y = 15 x^3 + 7/(2x^3) - x
dy/dx = 45 x^2 + 7/6 x^-2 - 1
Subscribe to:
Post Comments (Atom)
to get dy/dx
ReplyDelete=dy/du*du/dx
so du's would cancel
and dy/dx will remain
solution 3 is incorrect.first of all you will recognize that you have upstairs and downstairs in the equation.
ReplyDeleteyou will make the downstairs 7 / 2 x^3 into upstairs making it (7/2)* x^-3.
hence rewrite the equation as:
y = 15 x^3 + (7/2)*x^-3 + x
differentiating:
dy/dx =[(15*3)x^(3-1)] + [(-3*7/2)x^(-3-1)]
- [(1*1)x^(1-1)]
remember to be careful when working with minus signs and any number raise to the power of zero will give you 1
therefore:
dy/dx= 45x^2 - (21/2)x^-4 - 1
the final answer to solution 2 is correct but some steps are missing
ReplyDeletefirst we sub u for 6s^3+s
which make the equation P = ln(u)
therefore dp/du = 1/u
but we want dp/ds
so dp/ds = dp/du x du/ds
now using the equation u = 6s^3+s
du/ds = 18s^2+1
so dp/ds = (18s^2+1)x [1/(6s^3+s)]
or (18s^2+1)/(6s^3+s)
y = 15 x^3 + 7/(2x^3) - x
ReplyDeletethe solution is wrong, when you brought the downstairs of 7/(2x^3) to upstairs. It was suppose to be (7/2)x^3 not 7 *2 x^-3, so therefore the answer would be:
y = 15x^3 + (7/2)x^3 - x
where dy/dx = 45x^2 - ((21/2)x^-4) - 1
the solution is correct. remember when you carry a power from downstairs to upstairs if it is positive downstairs, it become negative upstairs hence the reason for 7/(2x^3) becoming (7/2)*x^-3.
ReplyDeletey = log base 3 (8x^7 + x)
ReplyDeleteu = 8 x^7 + x
dy/dx = 56 x^6 + 1
= (56 x^6 + 1) log base 3 e (8x^7 +x)
can anyone correct me if i am wrong. i am not sure if it is correct.
joh can u explain further i dont really catch on ur explaination????
ReplyDeletethe 1st one in solution 3:
ReplyDeletethe second line in solution 3 is correct because the 1st thing to do is to move all that is downstairs, upstairs.
however the last line is incorrect because the person wasnt aware of police. so it should of been:
= 45x^2 - 42x^-4 - 1
the second 1 in solution 3 is incorrect because the person did not differentiate the second term correct. they differentiated the term just as it was and made an error. this is why all terms should be carried upstairs when division is taking place. this is done to prevent errors like this one!!!
ReplyDeletehey can someone who knows how to do problem 1 and 2 PROPERLY explain it to me, it is confusing. plzz help!!!
ReplyDeleteTo mysticwings*, i kno that this is correct:
ReplyDeletey = log base 3 (8x^7 + x)
Substituting:
u = 8 x^7 + x
du/dx = 56 x^6 + 1
Rewriting the equation:
y = log base 3u
Then we didnt learn how to differentiate logs so i think up to here is correct.
I really don't know how to do these questions. can someone go through one of them step by step so i can try them on my own.
ReplyDeletethat will be very helpful.
thanks in advance
I myself am lost. someone take it one step at a time plez
ReplyDelete