Find the derivative of the function
y = sqrt of s^11 + 1
the entire thing is under the square root and and 1 is not in the exponent.
Is the answer 1/2 (s^11 +1)^-1/2(11s^10)?
To find the derivative of the function y = √(s^11 + 1), you can use the chain rule.
The chain rule states that if you have a function f(g(x)), the derivative of f(g(x)) with respect to x is given by the derivative of f with respect to g multiplied by the derivative of g with respect to x.
Let's apply the chain rule to finding the derivative of y = √(s^11 + 1):
1. Identify the inner function (s^11 + 1) and the outer function (√x).
2. Take the derivative of the outer function (√x) with respect to the inner function (s^11 + 1). This derivative is 1/(2√(s^11 + 1)).
3. Take the derivative of the inner function (s^11 + 1) with respect to s. The derivative of s^11 with respect to s is 11s^10, and the derivative of 1 with respect to s is 0.
4. Multiply the derivative of the outer function (√x) with respect to the inner function (s^11 + 1) by the derivative of the inner function (s^11 + 1) with respect to s.
Thus, the derivative of y = √(s^11 + 1) is (1/(2√(s^11 + 1)))(11s^10).
Therefore, the answer is (11s^10)/(2√(s^11 + 1)).