- #1
- 67
- 0
Homework Statement
hey guys, got a question. how do you differentiate y=ln(1+x^2)^1/2. any help would be appreciated, thanks
Homework Equations
answer is x/(1+x^2)
Go check your rules of differentiation again...geffman1 said:so the 1/2 just stays out the front without it being differentiate, i thought it dissapeared? thanks for the replys
The derivative of y = ln(1+x^2)^1/2 is given by the chain rule:
dy/dx = (1/2)(1+x^2)^(-1/2)(2x)(1+0) = x/(1+x^2)^1/2
To simplify the expression, you can use the power rule for logarithms:
ln(a^b) = b ln(a).
Applying this rule, we get ln(1+x^2)^1/2 = (1/2)ln(1+x^2).
The domain of y = ln(1+x^2)^1/2 is all real numbers, since both the natural logarithm and the square root function are defined for all positive real numbers.
Yes, ln(1+x^2)^1/2 can also be written as ln√(1+x^2) or ln(√(1+x^2)). Both forms are equivalent.
The derivative of y = ln(1+x^2)^1/2 can be used to find the rate of change of a function that involves the natural logarithm and the square root. This can be useful in fields such as physics, economics, and engineering where logarithmic and exponential functions are commonly used to model real-life phenomena.