Find the Derivative - d/dx y = cube root of 2x

Problem

d()/d(x)√(3,2*x)

Solution

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

√(3,2*x)=(2*x)(1/3)

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

d(2*x)/d(x)=1/3*(2*x)(1/3−1)⋅(d(2)*x)/d(x)

3. Differentiate the inner function 2*x and subtract the exponents.

1/3*(2*x)(−2/3)⋅2

4. Simplify the expression by multiplying the constants and moving the negative exponent to the denominator.

2/(3*(2*x)(2/3))

5. Convert the fractional exponent back into radical form.

2/(3√(3,(2*x)2))

6. Simplify the term inside the radical.

2/(3√(3,4*x2))

Final Answer

d(√(3,2*x))/d(x)=2/(3√(3,4*x2))

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