Calculus Differentiation Question

[ohlhauc1]

I am just learning calculus, and I have to differentiate a problem. I have worked on it and I have asked people, but they do not know. Here is what I have done thus far:

f(x) = 3x-6 – 8x5 + 9x2/5 + √7
f(x) = 3(dx-6/dx) – 8(dx5/dx) + 9(dx2/5/dx) + √7(d/dx)
f(x) = 3(-6x5) – 8(5x4) + 9(2/5x-3/5) + 0
f(x) = -18x5 – 40x4 + 18/5x-3/5

I am wondering if this is it, or whether I need to do more? If I need to do more, could you say which rule I should use or some other type of advice?

Thanks

P.S. If it is wrong, could you please tell me as well.

 

[berkeman]

Your notation is a bit confusing. What is the starting function f(x)? And are you asked to find d[f(x)]/dx? Are all the "x" in your equations the unknown "x", or are some of the multiplication symbols?

 

[Data]

if you mean that your function is

$$f(x) = 3x^{-6} - 8x^5 + 9x^{\frac{2}{5}}+\sqrt{7}$$

and you found that the derivative is

$$f^\prime (x) = -18x^5 - 40 x^4 + \frac{18}{5}x^{-\frac{3}{5}},$$

(I don't know why you've written f(x)= at every line when you are trying to differentiate)

then you have made a small error, because

$$\frac{d(x^{-6})}{dx} = -6x^{-7},$$

not $-6x^5$. Other than that it's ok (if I have translated your rather cryptic notation correctly - try to learn LaTeX: https://www.physicsforums.com/showthread.php?t=8997)