Asked by Steph
How exactly do you determine dy / dx ?
Maybe for this one: y = 2 / 3(x)^3
Maybe for this one: y = 2 / 3(x)^3
Answers
Answered by
bobpursley
You memorize the standard forms: In this case
if y=a x^b where b is any +- number
dy/dx= b*a* x<sup>b-1</sup>
here is an example:
y= 1/sqrt(x^2+1)
y= (x^2+1)^-.5
let u= x^2+1
dy/du= -.5 (u)^-1/5
dy/dx= dy/du*du/dx= -.5(x^2+1)^-1.5 * 2x
because du/dx= d (x^2+1)/dx= 2x
if y=a x^b where b is any +- number
dy/dx= b*a* x<sup>b-1</sup>
here is an example:
y= 1/sqrt(x^2+1)
y= (x^2+1)^-.5
let u= x^2+1
dy/du= -.5 (u)^-1/5
dy/dx= dy/du*du/dx= -.5(x^2+1)^-1.5 * 2x
because du/dx= d (x^2+1)/dx= 2x
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