Find the Derivative - d/d@VAR f(x) = square root of 3-2x

Problem

d()/d(x)√(,3−2*x)

Solution

1. Rewrite the square root as a power to make it easier to differentiate using the power rule.

√(,3−2*x)=(3−2*x)(1/2)

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

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

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

d(3−2*x)/d(x)=−2

4. Substitute the derivative of the inner function back into the expression.

1/2*(3−2*x)(−1/2)⋅(−2)

5. Simplify the expression by multiplying the constants and moving the negative exponent to the denominator.

−1⋅(3−2*x)(−1/2)=−1/((3−2*x)(1/2))

6. Convert the fractional exponent back into radical form.

−1/√(,3−2*x)

Final Answer

d(√(,3−2*x))/d(x)=−1/√(,3−2*x)

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