Confused with a fractional power

charlie_says

This is just one part of a long ten term differentiation problem. Anyhow cutting out the bits I do have no problem with, is this little chap. I can't seem to find why this is happening back in my fractional power notes, and this is given as the solution to this particular part.

-3/2x^3 = -3/2(x^-2)

surely it should be = -3/2(x^-3)? If not, how come? Why the x^-2?

Any ideas?

Thanks.....

planck2

let y = x^n.
I'm not sure if y = (-3/2)x^3 or -3/(2x^3). In anycase

dy/dx = nx^(n-1)

for example y =x^-1., dy/dx = -x^-2

y= x^-2, dy/dx = -2x^-3.

y = x^3, dy/dx = 3x^2

y =x^(-1/2), dy/dx = (-1/2)x^(-3/2), this is called a fractional power

charlie_says

planck2 wrote:

let y = x^n.
I'm not sure if y = (-3/2)x^3 or -3/(2x^3). In anycase

dy/dx = nx^(n-1)

for example y =x^-1., dy/dx = -x^-2

y= x^-2, dy/dx = -2x^-3.

y = x^3, dy/dx = 3x^2

y =x^(-1/2), dy/dx = (-1/2)x^(-3/2), this is called a fractional power

As it turns out it was a mistake by my tutor in the notes. Ho hum....

Thanks anyway...