- #1
autodidude
- 332
- 0
Differentiating y=x^x
x=ln(y)
I changed the base to e
x=\frac{ln(y)}{ln(x)}
xln(x) = ln(y)
e^{xln(x)} = y
e^{xln(x)}(1+ln(x) = \frac{dy}{dx}
The answer the calculator got was x^{x(1+ln(x))} so I noticed that since y=x^x and e^{xln(x)} = y, then I could replace it with x^x in the final answer
Is this an acceptable method? Is there any circular logic I missed? Could I leave it as is wihtout writing x^x?
x=ln(y)
I changed the base to e
x=\frac{ln(y)}{ln(x)}
xln(x) = ln(y)
e^{xln(x)} = y
e^{xln(x)}(1+ln(x) = \frac{dy}{dx}
The answer the calculator got was x^{x(1+ln(x))} so I noticed that since y=x^x and e^{xln(x)} = y, then I could replace it with x^x in the final answer
Is this an acceptable method? Is there any circular logic I missed? Could I leave it as is wihtout writing x^x?
