Find the Derivative - d/dx f(x) = square root of 7x^2-4x+3

Problem

d()/d(x)√(,7*x2−4*x+3)

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=7*x2−4*x+3

2. Apply the chain rule, which states that d()/d(x)*ƒ*(g(x))=ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function with respect to the inner function, treating the radicand as a single variable.

d(√(,u))/d(u)=1/(2√(,u))

4. Differentiate the inner function 7*x2−4*x+3 with respect to x using the power rule.

d(7*x2−4*x+3)/d(x)=14*x−4

5. Combine the results by multiplying the derivative of the outer function by the derivative of the inner function.

1/(2√(,7*x2−4*x+3))⋅(14*x−4)

6. Simplify the expression by factoring out a 2 from the numerator to cancel with the denominator.

(2*(7*x−2))/(2√(,7*x2−4*x+3))

Final Answer

d(√(,7*x2−4*x+3))/d(x)=(7*x−2)/√(,7*x2−4*x+3)

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