Question

Find derivative of f(x)=[x^(1/3)]*{[-7x^(2/3)]-[7x^(5/3)]+3}​

Answer 1

Answer:
`\bold{-7-14x-x^{-(2)/(3)}}`

Explanation:

`x^{(1)/(3)}[-7x^{(2)/(3)}-(7x^{(5)/(3)}+3)]\\\\\\\underline{\text{Distribute }x^{(1)/(3)}}\\-7x-7x^2-3x^{(1)/(3)}\\\\\\\underline{\text{Now find the derivative of each term:}}\\g(x)= 7x\implies g'(x)=7\\h(x) = -7x^2\implies h'(x)=-14x\\j(x)=-3x^{(1)/(3)}\implies j'(x)=-x^{-(2)/(3)}\\\\\underline{\text{Now combine the terms:}}\\f'(x) =g'(x)+h'(x)+j'(x)\quad =\large\boxed{7-14x-x^{-(2)/(3)}}`