Find the Derivative - d/dx 4 square root of x+18

Problem

d()/d(x)*4√(,x+18)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to differentiate.

√(,x+18)=(x+18)(1/2)

2. Apply the constant multiple rule, which allows the constant 4 to be moved outside the derivative.

d()/d(x)*4*(x+18)(1/2)=4⋅d()/d(x)*(x+18)(1/2)

3. Apply the power rule and the chain rule, where the derivative of un is n*u(n−1)⋅d(u)/d(x)

d()/d(x)*(x+18)(1/2)=1/2*(x+18)(−1/2)⋅d(x+18)/d(x)

4. Differentiate the inner function x+18 which results in 1

d(x+18)/d(x)=1

5. Multiply the terms together and simplify the expression.

4⋅1/2*(x+18)(−1/2)⋅1=2*(x+18)(−1/2)

6. Convert the negative exponent back into a radical in the denominator.

2*(x+18)(−1/2)=2/√(,x+18)

Final Answer

(d(4)√(,x+18))/d(x)=2/√(,x+18)

Want more problems? Check here!