Understanding Derivatives to Solving y = x^(x^2-7)

[Chadlee88]

Could som1 please explain how to derive y = x^(x^2-7)

I started using the chain rule but got stuck wif the x base.


thanx in advance

 

[HallsofIvy]

Do you mean "find the derivative"? (Yes, "derive f(x)" can mean that but often it means "derive this formula".)

Use "logarithmic differentiation". (In fact, I would expect a problem like this to be in a section of the book titled "logarithmic differentiation"!)

If y= x^{x^2- 7} then ln(y)= (x^2- 7)ln(x).
Can you differentiate both sides of that? Then solve for dy/dx.