Find the Derivative - d/dx square root of 1-6x

Problem

d(√(,1−6*x))/d(x)

Solution

1. Rewrite the square root as a power using the exponent 1/2

d(1−6*x)/d(x)

2. Apply the power rule and the chain rule by bringing the exponent to the front and subtracting 1 from the exponent.

1/2*(1−6*x)(−1/2)⋅d(1−6*x)/d(x)

3. Differentiate the inner function 1−6*x with respect to x

1/2*(1−6*x)(−1/2)⋅(−6)

4. Simplify the expression by multiplying the constants 1/2 and −6

−3*(1−6*x)(−1/2)

5. Rewrite the expression using a radical in the denominator to remove the negative exponent.

(−3)/√(,1−6*x)

Final Answer

d(√(,1−6*x))/d(x)=(−3)/√(,1−6*x)

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