Question

How do you find the derivative of `-7x^5(sqrt(x)) + (4/(x^2(sqrt(x))))`?

Answer 1

`(dy)/(dx)=-77/2sqrt(x^9)-10/sqrt(x^7)`

Explanation:

Write as: `y=(-7x^5xxx^(1/2))+(4xxx^(-2)xx x^(-1/2))`

`y=-7x^(11/2)+4x^(-5/2)`

`(dy)/(dx)=(-7xx11/2xx x^(11/2-1))+(4xx(-5/2)xxx^(-5/2-1))`

`(dy)/(dx)=-77/2 x^(9/2)-10x^(-7/2)`

Writing this in the same form as the question:

`(dy)/(dx)=-77/2sqrt(x^9)-10/sqrt(x^7)`