Differentiate the function 7 {x}^(3) + x / 6 √(x)

Question

Differentiate the function

`7 {x}^(3) + x / 6 √(x)`

Answer 1

There are two likely interpretations for the given function:

`f(x)=7x^3+\frac x{6\sqrt x}`

in which case you can write

`\frac x{6\sqrt x}=\frac x{6x^(1/2)}=\frac16x^(1/2)`

and the derivative is

`f'(x)=21x^2+\frac1{12}x^(-1/2)=21x^2+\frac1{12\sqrt x}`

Or, perhaps it is

`f(x)=(7x^3+x)/(6\sqrt x)=\frac76x^(5/2)+\frac16x^(1/2)`

`\implies f'(x)=(35)/(12)x^(3/2)+\frac1{12\sqrt x}`