Find the Derivative - d/dx y = square root of 5-7x

Problem

d()/d(x)√(,5−7*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=5−7*x

2. Apply the power rule and the chain rule, which states that d()/d(x)√(,u)=1/(2√(,u))⋅d(u)/d(x)

3. Differentiate the inner function 5 - 7xw*i*t*h*r*e*s(p)*e*c*t*t*o$.

d(5−7*x)/d(x)=−7

4. Substitute the inner derivative back into the chain rule formula.

d(y)/d(x)=1/(2√(,5−7*x))⋅(−7)

5. Simplify the expression by multiplying the constants.

d(y)/d(x)=−7/(2√(,5−7*x))

Final Answer

d(√(,5−7*x))/d(x)=−7/(2√(,5−7*x))

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