Find the Derivative - d/dx square root of 16-x^2

Problem

d(√(,16−x2))/d(x)

Solution

1. Rewrite the square root as a power to prepare for differentiation.

√(,16−x2)=(16−x2)(1/2)

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

d(16−x2)/d(x)=1/2*(16−x2)(−1/2)⋅d(16−x2)/d(x)

3. Differentiate the inner function 16−x2 with respect to x

d(16−x2)/d(x)=−2*x

4. Substitute the inner derivative back into the expression.

1/2*(16−x2)(−1/2)⋅(−2*x)

5. Simplify the expression by canceling the constants and moving the negative exponent to the denominator.

(−x)/((16−x2)(1/2))

6. Convert the fractional power back into radical form.

(−x)/√(,16−x2)

Final Answer

d(√(,16−x2))/d(x)=−x/√(,16−x2)

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