Find the Slope x=6

Problem

y=√(,x+3)

Solution

1. Identify the function to be differentiated, which is y=√(,x+3) or y=(x+3)(1/2)

2. Apply the power rule and the chain rule to find the derivative d(y)/d(x) which represents the slope of the tangent line at any point x

3. Differentiate the expression:

d(y)/d(x)=1/2*(x+3)(−1/2)

4. Simplify the derivative into a radical form:

d(y)/d(x)=1/(2√(,x+3))

5. Substitute the given value x=6 into the derivative to find the specific slope:

d(y)/d(x)=1/(2√(,6+3))

6. Calculate the final value:

d(y)/d(x)=1/(2√(,9))

d(y)/d(x)=1/(2*(3))

d(y)/d(x)=1/6

Final Answer

d(y)/d(x)=1/6

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