AwesomeSN said:Homework Statement
Differentiate, f(x)=71+x/1-x
Homework Equations
The Attempt at a Solution
Working this out, hoping it's right as I was going along, my final answer is 71+x/1-x * (2ln7)/1-x
The natural log function, denoted as ln(x), is the inverse of the exponential function. It represents the power to which the base number e (approximately 2.718) must be raised to obtain a given number.
To differentiate ln(x), you use the formula: d/dx(ln(x)) = 1/x. This means that the derivative of ln(x) is equal to 1 divided by x.
If you have ln(kx), where k is a constant, the derivative is equal to 1/k. This is because the constant k can be factored out of the derivative.
The natural log function can only be negative for values of x between 0 and 1. For all other values, the natural log function is positive. This is because the graph of ln(x) crosses the x-axis at 1 and approaches negative infinity as x approaches 0.
The natural log function uses the base e, while other logarithmic functions use different bases such as 10 or 2. The properties and rules for differentiating natural log are unique to its base of e, while other logarithmic functions have their own set of rules and properties.