Find the Derivative - d/d@VAR f(X) = square root of 1-2x

Problem

d(√(,1−2*x))/d(x)

Solution

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

√(,1−2*x)=(1−2*x)(1/2)

2. Apply the power rule and the chain rule by differentiating the outer function while keeping the inner function the same.

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

3. Differentiate the inner function 1−2*x with respect to x

d(1−2*x)/d(x)=−2

4. Multiply the results of the power rule and the derivative of the inner function.

1/2*(1−2*x)(−1/2)⋅(−2)=−(1−2*x)(−1/2)

5. Simplify the expression by moving the negative exponent to the denominator as a square root.

−(1−2*x)(−1/2)=−1/√(,1−2*x)

Final Answer

d(√(,1−2*x))/d(x)=−1/√(,1−2*x)

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