HHenderson90 said:Homework Statement
Find y' of
y= 1-3ln(7x)/x^4
Homework Equations
The Attempt at a Solution
I used the quotient rule and got:
y'=x^4*d/dx(1-3ln(7x)-(1-3ln(7x)*d/dx(x^4)/(x^4)2
which is: x^4*(0-3*1/7x*7)-(1-3ln(7x))*4x^3/x^8
simplified to: 3x^4/x-1+3ln(7x)*4x^3
3x^3-4x^3+12x^3ln(7x)/x^8
take out the x^3 from the denominator and the numerator and I get the answer:
y=-1+12ln(7x)/x^5
The website I use to do my calculus homework says this is wrong, where is my error?
The quotient rule is a formula used to find the derivative of a function that is a ratio of two other functions. It states that the derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all over the square of the denominator.
To apply the quotient rule to a natural log function, you first need to rewrite the function as the quotient of two functions. For example, if you have ln(x), you can rewrite it as (lnx)/1. Then, you can use the quotient rule to find the derivative by taking the derivative of the numerator (lnx) and the denominator (1) and plugging them into the formula.
Yes, the quotient rule can be used for any type of function, as long as it can be written as the quotient of two other functions. This includes polynomial functions, trigonometric functions, exponential functions, and more.
Yes, there is another method called the product rule, which is used when the function is a product of two other functions. It states that the derivative of the product of two functions is equal to the first function times the derivative of the second function plus the second function times the derivative of the first function.
You can check your answer by using the quotient rule to find the derivative of the function and then comparing it to the derivative found using other methods, such as the product rule or by simplifying the function and using the power rule. If the answers match, then you can be confident that you have correctly applied the quotient rule.