Question

Question #73545

Answer 1

`dy/dx=5/2x^(-1/2)-3/2x^(1/2)-5/6x^(3/2)`

Explanation:

We could differentiate f(x) using the `color(blue)"product rule"`

However. if we distribute we can use the 'simpler' `color(blue)"power rule"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))larr" power rule"`

`rArry=x^(1/2)(5-x-1/3x^2)`

`color(white)(xxxx)=5x^(1/2)-x^(3/2)-1/3x^(5/2)`

`rArrdy/dx=5/2x^(-1/2)-3/2x^(1/2)-5/6x^(3/2)`

you may wish to take this further and give the answer with positive exponents .