Find the Derivative - d/dx y = cube root of 1+8x

Problem

d()/d(x)√(3,1+8*x)

Solution

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

√(3,1+8*x)=(1+8*x)(1/3)

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

d(1+8*x)/d(x)=1/3*(1+8*x)(−2/3)⋅d(1+8*x)/d(x)

3. Differentiate the inner function 1+8*x with respect to x

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

4. Multiply the results together to find the derivative.

1/3*(1+8*x)(−2/3)⋅8=8/3*(1+8*x)(−2/3)

5. Simplify the expression by moving the negative exponent to the denominator.

8/(3*(1+8*x)(2/3))=8/(3√(3,(1+8*x)2))

Final Answer

d(√(3,1+8*x))/d(x)=8/(3√(3,(1+8*x)2))

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