Question

How do you find the derivative of `y = ((x^5)/6) + (1/(10x^3))`?

Answer 1

`f'(x) = 5/6x^4 - 3/(10x^4)`

Explanation:

Given: `f(x)=y=color(red)((x^5)/6) + color(blue)(1/(10x^3))`
Required: `f'(x)=(dy)/dx`?
Definition and principles:
`color(red)((dx^n)/dx=nx^(n-1))` and
`color(blue)(d/dx(1/n^k)=-kx^(-k-1))`

Solution strategy: Apply the power rules above:
`(dy)/dx= color(red)(5/6x^4) + 1/10color(blue)((-3/x^4 ))`

`f'(x) = 5/6x^4 - 3/(10x^4)`