Question #73545

1 Answer
Feb 4, 2017

Answer:

#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 .