Thread: Finding the derivatives of functions

I have 2 problems I was confused with.
1. f(x)=(2x²-3x+1)/x
2. f(x)=x^4/5

This is what I did for the first one:
I moved the x up, which turns into 2x²-3x+1+x^-1
Then I multipled the coefficient by the exponents, and subtracted 1 from the exponent: 4x-3+1+x^-2
But I was wondering, what do you do for the 1 here?

And for the second one:
Same thing, multipled exponent into coefficient: (4/5)x^-1/5
Then 1/(4/5x⁵)
Then I got lost here... the answer in the book is: 4/(5x^1/5)
It looks like the denominator just had the exponent switched into the positive, is that the right way to move it though?

your algebra needs work ...


, now take the derivative.


, only the x has a negative exponent

Originally Posted by skeeter

your algebra needs work ...


, now take the derivative.


, only the x has a negative exponent

Oh thanks!
So then the derivative would be 2-x^-2, which then becomes 2-(1/x²) right?

Originally Posted by Chaim

So then the derivative would be 2-x^-2, which then becomes 2-(1/x²) right?

correct

Originally Posted by skeeter

correct

Thanks!

Now I think I'm starting to get how to find derivatives of a function.