For some reason I cannot get this darned thing to work out right...
Differentiate:
Sq.Rt. (x + sq.rt. (x) )
It seems to me like it should be:
1 / [ 4 * sq.rt.(x + sq.rt. (x)) * sq.rt. (x) ]
BUT, calculator indicates:
[2 * sq.rt. (x) + 1] / [4 * sq.rt. (x) * sq.rt. {sq.rt. (x) + (sq.rt. (x) + 1) } ]
I cannot figure out what the heck i'm doing wrong. I'm using chain rule and differentiating whole function, to get 1 / [2 * sq.rt. {x + sq.rt. (x) } ] for the first function, then 1 / [2 * sq.rt. (x) ] for the second one, multiplying them to get the above result. I tried graphing them on the calculator and comparing the slope of the tangent line, as computed by my calculator, of the initial function at x=0.75 and it matches the value of what my calculator indicates if the correct derivative at x=0.75 but it does not match what my work indicates is correct.
Would greatly appreciate any help.
Differentiate:
Sq.Rt. (x + sq.rt. (x) )
It seems to me like it should be:
1 / [ 4 * sq.rt.(x + sq.rt. (x)) * sq.rt. (x) ]
BUT, calculator indicates:
[2 * sq.rt. (x) + 1] / [4 * sq.rt. (x) * sq.rt. {sq.rt. (x) + (sq.rt. (x) + 1) } ]
I cannot figure out what the heck i'm doing wrong. I'm using chain rule and differentiating whole function, to get 1 / [2 * sq.rt. {x + sq.rt. (x) } ] for the first function, then 1 / [2 * sq.rt. (x) ] for the second one, multiplying them to get the above result. I tried graphing them on the calculator and comparing the slope of the tangent line, as computed by my calculator, of the initial function at x=0.75 and it matches the value of what my calculator indicates if the correct derivative at x=0.75 but it does not match what my work indicates is correct.
Would greatly appreciate any help.