Find the Derivative - d/dx y = square root of 6+7x

Problem

d()/d(x)√(,6+7*x)

Solution

1. Rewrite the radical expression using a fractional exponent to prepare for differentiation.

√(,6+7*x)=(6+7*x)(1/2)

2. Apply the chain rule, which states that the derivative of un is n*u(n−1)⋅d(u)/d(x)

d(6+7*x)/d(x)=1/2*(6+7*x)(−1/2)⋅d(6+7*x)/d(x)

3. Differentiate the inner function 6+7*x with respect to x

d(6+7*x)/d(x)=7

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

1/2*(6+7*x)(−1/2)⋅7

5. Simplify the expression by moving the term with the negative exponent to the denominator and converting it back to radical form.

7/(2√(,6+7*x))

Final Answer

d(√(,6+7*x))/d(x)=7/(2√(,6+7*x))

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