Final answer:
To find the differential of the function y = √(x + 7), use the chain rule.
Step-by-step explanation:
To find the differential of the function y = √(x + 7), we can use the chain rule. The chain rule states that if y = f(g(x)), then the differential of y is given by dy = f'(g(x))*g'(x)*dx. In this case, f(g(x)) = √(x + 7), so g(x) = x + 7.
To find f'(g(x)), we take the derivative of f(x) with respect to x and substitute g(x) = x + 7:
f'(g(x)) = ½(x + 7)^(-½) = ½/√(x + 7)
The derivative of g(x) = x + 7 with respect to x is simply 1.
Substituting these values into the chain rule formula, we have dy = ½/√(x + 7)*1*dx = ½/√(x + 7)*dx.