Find the Derivative - d/dx 3 square root of x+5

Problem

d()/d(x)*3√(,x+5)

Solution

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

3√(,x+5)=3*(x+5)(1/2)

2. Apply the constant multiple rule to move the constant outside of the derivative.

d()/d(x)*3*(x+5)(1/2)=3⋅d()/d(x)*(x+5)(1/2)

3. Apply the power rule and the chain rule, where the derivative of the outer function is 1/2*(x+5)(−1/2) and the derivative of the inner function (x+5) is 1

3⋅1/2*(x+5)(−1/2)⋅1

4. Simplify the expression by multiplying the constants and moving the negative exponent to the denominator as a square root.

3/(2*(x+5)(1/2))=3/(2√(,x+5))

Final Answer

(d(3)√(,x+5))/d(x)=3/(2√(,x+5))

Want more problems? Check here!