Find the Derivative - d/dx square root of 6+5x

Problem

d(√(,6+5*x))/d(x)

Solution

1. Rewrite the square root expression using a fractional exponent to prepare for the power rule.

√(,6+5*x)=(6+5*x)(1/2)

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

d(6+5*x)/d(x)=1/2*(6+5*x)(−1/2)⋅d(6+5*x)/d(x)

3. Differentiate the inner function 6+5*x with respect to x

d(6+5*x)/d(x)=5

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

1/2*(6+5*x)(−1/2)⋅5

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

5/(2√(,6+5*x))

Final Answer

d(√(,6+5*x))/d(x)=5/(2√(,6+5*x))

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