how to find the second derivative of quotient rule?
f(x): 700v^2 + 3450/v
f'(x) : 700v^2 -3450/v^2
f"'(x) : ???
sorry typo error above, question is,
f(x): 700v^2 + 34500/v
f'(x) : 700v^2 -34500/v^2
f"'(x) : ???
the way you typed it ....
f'(x) = 1400v - 3450/v^2 or 1400v - 3450v^-2
f''(x) =1400 + 6900v^-3
IF you meant f(x) = (700v^2 + 3450)/v
I would change it to
f(x) = 700v + 3400v^-1
f'(x) = 700 - 3400v^-2
f''(x) = 6800v^-3 or 6800/v^2
The question should be:
f(x): 700v^2 + 34500/v
f'(x) : 700v^2 -34500/v^2
f''(x) : ???
You missed my point, the issue was not whether it was 3450 or 34500, the point was the use of brackets.
Did you not look at my reply?
simply change 3450 to 34500 and follow the steps.
You derivative would be correct if you had placed it in brackets , such as
f'(x) = (700v^2 - 34500)/v^2
which would reduce to
f'(x) = 700 - 34500/v^2 = 700 - 34500v^-2
then f''(x) = 69000/v^3
pls ignore the above question...
to make it clearer for the question, it is...
f(x): (700v^2 + 34500)/v
f'(x) : (700v^2 -34500)/v^2
f''(x) : ???
i got the answer!! thank you!!!
To find the third derivative, or f''(x), of a function using the quotient rule, you'll need to differentiate the function twice.
First, let's write the function using the quotient rule:
f(x) = (700v^2 + 3450/v)
To find f'(x):
1. Differentiate the numerator (700v^2) with respect to v, treating v as the variable and 3450/v as a constant. The derivative of v^2 is 2v, so the numerator becomes 700 * 2v = 1400v.
2. Differentiate the denominator (3450/v) with respect to v. The derivative of v is 1/v, so the denominator becomes 3450 * (1/v) = 3450/v.
Therefore, f'(x) = (1400v - 3450/v).
To find f''(x):
1. Take the derivative of f'(x) with respect to v.
Differentiate the numerator (1400v) with respect to v. The derivative of v is 1, so the numerator becomes 1400 * 1 = 1400.
Differentiate the denominator (-3450/v) with respect to v. The derivative of 1/v is -1/v^2, so the denominator becomes -3450 * (-1/v^2) = 3450/v^2.
Therefore, f''(x) = (1400 + 3450/v^2) or 1400 + (3450/v^2).
The result above is the second derivative, or f''(x), of the given function using the quotient rule.