Find the Derivative - d/dx fifth root of 7x

Problem

d(√(5,7*x))/d(x)

Solution

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

√(5,7*x)=(7*x)(1/5)

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

d(7*x)/d(x)=1/5*(7*x)(1/5−1)⋅(d(7)*x)/d(x)

3. Differentiate the inner function 7*x and simplify the exponent.

1/5*(7*x)(−4/5)⋅7

4. Combine the constants and rewrite the expression with a positive exponent in the denominator.

7/(5*(7*x)(4/5))

5. Convert the fractional exponent back into radical form if desired.

7/(5√(5,(7*x)4))

Final Answer

d(√(5,7*x))/d(x)=7/(5√(5,2401*x4))

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