The equation of the curve is y = 15x^3/2 - x^5/2. Find dy/dx.

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to differentiate the function with respect to x such that:

`(dy)/(dx) = 15*3x^2/2 - 5x^4/2`

`(dy)/(dx) = 45x^2/2 - 5x^4/2`

Notice that you need to use power property to differentiate the function such that:

`y= x^n =gt(dy)/(dx) = (x^n)' `

 

Hence, differentiating the function yields `(dy)/(dx) = (45x^2 - 5x^4)/2.`

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ksri | High School Teacher | (Level 3) eNoter

Posted on

y = 15 x^3/2  - x^3/2

dy/dx = 15*3/2 x^(3/2-1)  - 5/2 x^(5/2-1)

          =45/2 x^1/2  - 5/2 x^3/2

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