_____________ / x 8* / 5*x + - - 1 \/ 5
8*sqrt(5*x + x/5 - 1)
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result is:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
104 ------------------- _____________ / x 5* / 5*x + - - 1 \/ 5
-1352 ----------------- 3/2 / 26*x\ 25*|-1 + ----| \ 5 /