- #1
M.Qayyum
- 13
- 0
Homework Statement
1) ln { (x^2+x+1) / ( x^2-x+1) } here ln = natural log
2) x^2+x^(2y)=c here c=constant
Mark44 said:Show us your attempt at a solution.
x2y [itex]\neq[/itex] 2y ln(x).M.Qayyum said:My attempt at 2)
x^2+x^(2y)=c
x^2+2ylnx=c
M.Qayyum said:diff wrt x
2+(2lnx+1/x.2y.y')=0
1/x.2y.y'=-2-2lnx
y'= -2(lnx+1)x / 2y
is this correct and i can't understand the question no. one and how to start it's differentiation.
When you differentiate with respect to x, you are finding the derivative of a function with respect to the independent variable x. This means that you are finding how the output of the function changes as the input x changes.
In many scientific fields, such as physics and engineering, it is important to understand how a quantity changes in relation to another quantity. Differentiating with respect to x allows us to quantify this relationship and make predictions about how the system will behave.
The process of differentiating with respect to x involves using specific rules and formulas, such as the power rule and chain rule, to find the derivative of a function. This involves taking the limit of the change in the function's output over the change in the input, as the change in the input approaches zero.
Differentiation with respect to x has many applications in various fields, including physics, engineering, economics, and biology. It can be used to find rates of change, optimize functions, model physical systems, and analyze data.
To improve your skills in differentiating with respect to x, it is important to practice using different rules and formulas and to apply them to a variety of functions. You can also seek help from a tutor or online resources to better understand the concepts and techniques involved in differentiation.