Find the Derivative - d/dx y = square root of 3-7x

Problem

d()/d(x)√(,3−7*x)

Solution

1. Identify the function as a composition of functions where the outer function is the square root, u(1/2) and the inner function is u=3−7*x

2. Apply the power rule and the chain rule to differentiate the expression.

3. Differentiate the outer function with respect to the inner function.

d()/d(u)*u(1/2)=1/2*u(−1/2)

4. Differentiate the inner function with respect to x

d()/d(x)*(3−7*x)=−7

5. Combine the results using the chain rule formula d(y)/d(x)=d(y)/d(u)⋅d(u)/d(x)

d(y)/d(x)=1/2*(3−7*x)(−1/2)⋅(−7)

6. Simplify the expression by moving the negative exponent to the denominator and combining the constants.

d(y)/d(x)=−7/(2√(,3−7*x))

Final Answer

d(√(,3−7*x))/d(x)=−7/(2√(,3−7*x))

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