Simplify using basic simplification. y=x^(1-x)
I did try and got it wrong and I'm unsure on how to go about the problem.
Can't be taken any further, unless you want to use logs
Don't know what you mean by "basic simplification".
How would you use logs?
y = x^(1-x)
take ln of both sides
ln y = ln (x^(1-x)
= (1-x)(ln x)
ln y = (1-x)(ln x)
don't really see what can be gained by that, unless you were asked to find the derivative of the original.
Now it can be done.
If I were to find the derivative, would I derive ln y=(1-x)(lnx)? How would you derive this problem?
To simplify the expression y = x^(1-x), let's follow these steps using basic simplification techniques:
Step 1: Rewrite the exponent as a fraction.
y = x^(1/x - 1)
Step 2: Apply the exponent rule for division of exponents.
y = x^1/x * x^(-1)
Step 3: Simplify the exponents.
y = (x^1)^1/x * x^(-1)
Step 4: Simplify further.
y = x^(1/x) * 1/x
So, the simplified expression for y is y = x^(1/x) * 1/x.