Find the Derivative - d/dx f(x) = square root of 4-x^2

Problem

d(√(,4−x2))/d(x)

Solution

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

√(,4−x2)=(4−x2)(1/2)

2. Apply the chain rule, which states that the derivative of un is n*u(n−1)⋅d(u)/d(x)

d(4−x2)/d(x)=1/2*(4−x2)(−1/2)⋅d(4−x2)/d(x)

3. Differentiate the inner function 4−x2 with respect to x

d(4−x2)/d(x)=−2*x

4. Substitute the inner derivative back into the expression.

1/2*(4−x2)(−1/2)⋅(−2*x)

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

(−2*x)/(2√(,4−x2))

6. Reduce the fraction to its simplest form.

(−x)/√(,4−x2)

Final Answer

d(√(,4−x2))/d(x)=−x/√(,4−x2)

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