Question

Why does the derivative of x^3/2 + 1 = 3/2x^1/2?

Answer 1

\[ x^{3/2}+1 = \frac{ 3 }{ 2 }x ^{1/2}\]

Answer 2

I understand by the power rule that i pull the 3/2s out front and then subtract from the exponent and get the 3/2x^1/2, but where does the 1 go?

Answer 3

the derivative of one is zero

Answer 4

always?

Answer 5

adding one to the end raises the function up by one unit,but it does not change its shape
the slopes are still the same

Answer 6

the derivative of a constant is zero, just like the slope of a horizontal line is zero

Answer 7

well my book shows the derivative of 2+x^-1 = -x^-2
Where did the 2 go?

Answer 8

two is a constant

Answer 9

oh ok that makes sense

Answer 10

"derivative of constant =0"

Answer 11

so if i'm taking the dervative of any constant number than its always 0?

Answer 12

see above ^

Answer 13

thanks! would have been nice for my teacher to tell me that!

Answer 14

think of the graph of \(y=x^2\) and the graph of \(y=x^2+2\)
the shapes are identical, the second is just two units above the first

Answer 15

yes, the derivative of any constant is zero, so the derivative of \(x^2\) and \(x^2+3\) and \(x^2-1\) are all \(2x\)

Answer 16

Thanks!

Answer 17

think of it like this dy/dx measures change of y with respect to x..if y= a constant then there is no change at all .

so derivative=0