Find the Derivative - d/dx 8 square root of x

Problem

d()/d(x)*8√(,x)

Solution

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

√(,x)=x(1/2)

2. Apply the constant multiple rule, which allows the constant 8 to be moved outside the derivative.

d()/d(x)*8*x(1/2)=8d(x(1/2))/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) where n=1/2

8d(x(1/2))/d(x)=8⋅1/2*x(1/2−1)

4. Simplify the coefficient and the exponent.

4*x(−1/2)

5. Rewrite the expression using positive exponents and radical notation.

4/(x(1/2))=4/√(,x)

Final Answer

(d(8)√(,x))/d(x)=4/√(,x)

Want more problems? Check here!