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

Problem

d(√(,8*x))/d(x)

Solution

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

√(,8*x)=(8*x)(1/2)

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

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

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

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

4. Substitute the derivative of the inner function back into the expression.

1/2*(8*x)(−1/2)⋅8

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

4*(8*x)(−1/2)

4/√(,8*x)

6. Simplify the radical in the denominator further if possible.

√(,8*x)=√(,4⋅2*x)=2√(,2*x)

4/(2√(,2*x))=2/√(,2*x)

Final Answer

d(√(,8*x))/d(x)=2/√(,2*x)

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