Find the Derivative - d/dx fifth root of 6x

Problem

d(√(5,6*x))/d(x)

Solution

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

√(5,6*x)=(6*x)(1/5)

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

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

3. Differentiate the inner function 6*x and subtract the exponents.

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

1/5−1=−4/5

4. Substitute these values back into the expression.

1/5*(6*x)(−4/5)⋅6

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

6/(5*(6*x)(4/5))

Final Answer

d(√(5,6*x))/d(x)=6/(5√(5,(6*x)4))

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