Find the derivative of
y = 2√s7 + 13
To find the derivative of the given function, we can use the power rule of differentiation, which states that the derivative of x^n (where n is a constant) is equal to n*x^(n-1).
First, let's rewrite the given function in a simpler form:
y = 2√(7s) + 13
Next, let's break down the function into two parts:
y = 2 * √(7s) + 13
The derivative of the constant term 13 is zero, since a constant has a derivative of zero.
Next, we need to find the derivative of the first term, which is 2 * √(7s).
Using the power rule, we differentiate √(7s) with respect to s.
Let u = 7s, then √(7s) = √u
Using the chain rule, the derivative of √u is 1/(2√u) * du/ds.
Now, let's take the derivative of u with respect to s:
du/ds = 7
Plugging this value back into our equation, we get:
1/(2√u) * 7
Multiplying the constant and simplifying, we have:
7/(2√u)
Since our original function was y = 2 * √(7s) + 13, the derivative of y with respect to s is:
dy/ds = 7/(2√(7s))
Therefore, the derivative of y = 2√(7s) + 13 with respect to s is dy/ds = 7/(2√(7s)).