Find the Derivative - d/dx square root of 2-6x

Problem

d(√(,2−6*x))/d(x)

Solution

1. Rewrite the square root as a power using the rule √(,u)=u(1/2)

d(2−6*x)/d(x)

2. Apply the power rule and the chain rule, which states d(un)/d(x)=n*u(n−1)⋅d(u)/d(x)

1/2*(2−6*x)(−1/2)⋅d(2−6*x)/d(x)

3. Differentiate the inner function 2−6*x with respect to x

1/2*(2−6*x)(−1/2)⋅(−6)

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

−3*(2−6*x)(−1/2)

5. Rewrite the expression using a positive exponent and radical notation.

(−3)/√(,2−6*x)

Final Answer

d(√(,2−6*x))/d(x)=(−3)/√(,2−6*x)

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