w=4e^sqrt(s) Find the derivative of the function.
w = 4e^√s
d/ds e^u = e^u du/ds
Here we have u = s^(1/2)
so, du/ds = 1/2 s^(-1/2) = 1/(2√s)
so, dw/ds = 4 e^√s * 1/(2√s)
= 2/√s e^√s
To find the derivative of the function w = 4e^(√s), we can use the chain rule. The chain rule states that if we have a function of the form f(g(x)), then the derivative is given by f'(g(x)) * g'(x).
In this case, we have f(g) = 4e^g and g(s) = √s.
First, we find the derivative of g(s). The derivative of √s is given by 1/(2√s) using the power rule.
Next, we find the derivative of f(g). The derivative of e^g is simply e^g.
Finally, we apply the chain rule. Multiplying the derivatives together, we get:
w' = f'(g(s)) * g'(s) = e^(√s) * 1/(2√s) = e^(√s) / (2√s)
So, the derivative of the function w = 4e^(√s) is w' = e^(√s) / (2√s).