# How do you find the slope of a tangent line to the graph of the function # f(x) = 1/sqrt(6x)# at x=9?

Start by finding the derivative.

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To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. In this case, to find the slope of the tangent line to the graph of f(x) = 1/sqrt(6x) at x = 9, we need to find the derivative of the function and evaluate it at x = 9.

First, we can rewrite the function as f(x) = (6x)^(-1/2).

To find the derivative, we can use the power rule for differentiation. The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

Applying the power rule to our function f(x) = (6x)^(-1/2), we get f'(x) = (-1/2)*(6x)^(-1/2 - 1) = (-1/2)*(6x)^(-3/2).

Now, we can evaluate the derivative at x = 9. Substituting x = 9 into the derivative expression, we get f'(9) = (-1/2)*(6*9)^(-3/2) = (-1/2)*(54)^(-3/2).

Therefore, the slope of the tangent line to the graph of f(x) = 1/sqrt(6x) at x = 9 is (-1/2)*(54)^(-3/2).

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