Question

How do I find dy/dx of the following?

Answer 1

`\displaystyle(dy)/(dx) \ = \ 3x^(2) \ + \ \displaystyle\frac{1}{2\sqrt{x^(3)}} \ - \ \displaystyle(12)/(x^(5))`

Explanation:

`y \ = \ x^(3) \ - \ \displaystyle(1)/(√(x)) \ + \ \displaystyle(3)/(x^(4)) \\ \\ y \ = \ x^(3) \ - \ x^{-(1)/(2)} \ + \ 3x^(-4) \\ \\ \displaystyle(dy)/(dx) \ = \ 3x^(3 \ - \ 1) \ - \ \left(-\displaystyle(1)/(2)\right)x^{-(1)/(2) \ - \ 1} \ + \ \left(-4 \ * \ 3\right)x^(-4-1)`

`\displaystyle(dy)/(dx) \ = \ 3x^(2) \ + \ \displaystyle(1)/(2)x^{-(3)/(2)} \ - \ 12x^(-5) \\ \\ \displaystyle(dy)/(dx) \ = \ 3x^(2) \ + \ \displaystyle\frac{1}{2\sqrt{x^(3)}} \ - \ \displaystyle(12)/(x^(5))`