Question

Find the derivative of the function y = √(-8 + 3x).

a) dy/dx = (3/2)√(3x - 8)
b) dy/dx = (3/2)√(3x + 8)
c) dy/dx = (3/2)√(8 - 3x)
d) dy/dx = (-3/2)√(8 - 3x)

Answer 1

The derivative of the function y = √(-8 + 3x) is (3/2)√(3x - 8).

Step-by-step explanation:

To find the derivative of the function y = √(-8 + 3x), we can use the power rule for differentiation. The power rule states that if we have a function of the form y = x^n, then the derivative dy/dx is given by dy/dx = n*x^(n-1).

1. In this case, we have y = √(-8 + 3x), which can be rewritten as y = (-8 + 3x)^(1/2).
2. Applying the power rule, we get dy/dx = (1/2)*(-8 + 3x)^(1/2-1)*3 = (3/2)*(-8 + 3x)^(-1/2)*3 = (3/2)*√(-8 + 3x)/-2 = -(3/2)√(-8 + 3x)/2.
3. Simplifying further, we find that dy/dx = (3/2)√(3x - 8).