differentiate(solve)

Question

y=square root x+3

Answer 1

To differentiate the given equation, y = sqrt(x+3), we need to first recognize that the square root function is equivalent to raising the quantity inside the square root to the power of 1/2.

So we rewrite the equation as: y = (x+3)^(1/2)

Next, we differentiate term by term using the power rule of differentiation:

dy/dx = (1/2)(x+3)^(-1/2) * d/dx(x+3)
dy/dx = (1/2)(x+3)^(-1/2) * 1
dy/dx = 1/(2√(x+3))

Therefore, the derivative of y = sqrt(x+3) with respect to x is dy/dx = 1/(2√(x+3))