Find the Derivative - d/d@VAR f(x) = square root of 1-6x

Problem

d()/d(x)√(,1−6*x)

Solution

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

√(,1−6*x)=(1−6*x)(1/2)

2. Apply the Power Rule and the Chain Rule by differentiating the outer function and then multiplying by the derivative of the inner function.

d(1−6*x)/d(x)=1/2*(1−6*x)(−1/2)⋅d(1−6*x)/d(x)

3. Differentiate the inner expression 1−6*x

d(1−6*x)/d(x)=−6

4. Multiply the results together.

1/2*(1−6*x)(−1/2)⋅(−6)=−3*(1−6*x)(−1/2)

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

−3*(1−6*x)(−1/2)=(−3)/√(,1−6*x)

Final Answer

d(√(,1−6*x))/d(x)=(−3)/√(,1−6*x)

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