Evaluate f'(1) for the function f(x) = (x^2 + 2)^5

First, we must differentiate the function. To do this we must let the contents of the bracket be equal to 'u'. We now can produce two equations, one by subbing in 'u' into the function f(x) to give us u^5. The other equation is u = (x^2 + 2). From the chain rule we can recognize that the differential of the function with respect to x (which is what we want) is equal to the differential of the function with respect to u, multiplied by the differential of 'u' with respect to x. By doing this we obtain 5u^4 * 2x = 10xu^4 . By subbing in 'u' , we get the final form in terms of x which is 10x(x^2 + 2)^4. Now to obtain the value of the differential when x=1 by subbing it into the final form above, this gives us a value for df/dx of 810.