Find the Derivative - d/d@VAR g(x) = square root of 7-x

Problem

d()/d(x)√(,7−x)

Solution

1. Rewrite the square root function as a power to prepare for the chain rule.

√(,7−x)=(7−x)(1/2)

2. Apply the power rule to the outer function, which is the exponent 1/2

d(7−x)/d(x)=1/2*(7−x)(−1/2)⋅d(7−x)/d(x)

3. Apply the chain rule by finding the derivative of the inner function 7−x

d(7−x)/d(x)=−1

4. Multiply the results of the power rule and the chain rule.

1/2*(7−x)(−1/2)⋅(−1)=−1/2*(7−x)(−1/2)

5. Simplify the expression by moving the negative exponent to the denominator and converting back to radical form.

−1/(2√(,7−x))

Final Answer

d(√(,7−x))/d(x)=−1/(2√(,7−x))

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