Find the Derivative - d/dx square root of 1-4x

Problem

d(√(,1−4*x))/d(x)

Solution

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

√(,1−4*x)=(1−4*x)(1/2)

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

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

3. Differentiate the inner function 1−4*x with respect to x

d(1−4*x)/d(x)=−4

4. Multiply the results from the previous steps.

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

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

−2*(1−4*x)(−1/2)=(−2)/√(,1−4*x)

Final Answer

d(√(,1−4*x))/d(x)=−2/√(,1−4*x)

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