5 --------------- ___ ___ \/ 2 *\/ x + 3
5/(sqrt(2)*sqrt(x) + 3)
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:
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 the constant is zero.
The result is:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
___ -5*\/ 2 -------------------------- 2 ___ / ___ ___ \ 2*\/ x *\\/ 2 *\/ x + 3/
/ ___ \ | 1 \/ 2 | 5*|------------------- + ------| | / ___ ___\ 3/2| \x*\3 + \/ 2 *\/ x / 4*x / -------------------------------- 2 / ___ ___\ \3 + \/ 2 *\/ x /
/ ___ ___ \ |\/ 2 4 4*\/ 2 | -15*|----- + -------------------- + -----------------------| | 5/2 2 / ___ ___\ 2| | x x *\3 + \/ 2 *\/ x / 3/2 / ___ ___\ | \ x *\3 + \/ 2 *\/ x / / ------------------------------------------------------------ 2 / ___ ___\ 8*\3 + \/ 2 *\/ x /