How do you find the derivative of 4sqrt(x-3) + x^5/(2x)?

1 Answer
May 20, 2015

The first step here would be to write the equation in a way that is easier to understand:

f(x) =4sqrt(x-3) + x^5/(2x) = 4(x-3)^(1/2) + x^4/2

now we solve for f'(x)

we can use the chain rule in the first section. The chain rule states that:

(dy)/(du)*(du)/(dx)=(dy)/(dx)

Naming u=(x-3) and then using the chain rule, we get:

color(red)(d/(dx) 4(x-3)^(1/2) = 2(x-3)^(-1/2)(1) = 2(x-3)^(-1/2))

and the second section would be:

color(blue)(d/dx x^4/2 = 2x^3)

now we also know that

f'(x) = d/(dx) 4(x-3)^(1/2) + d/dx x^4/2

so we can now just drop in our two results:

f'(x) = 2(x-3)^(-1/2) + 2x^3