What is the derivative of the square root of x?

Answer

The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half.

The derivative of x to the power of n is n times x to the power of n minus one. This can be used for x to the power of one-half. One-half minus one is negative one-half, so the derivative is one-half times x to the power of negative one-half. X to the negative n equals one divided by x to the n, so the derivative is one-half times one divided by x to the power of one-half. Since x to the power of one-half is the square root of x, the final result is one-half times one divided by the square root of x.

Q&A Related to "What is the derivative of the square root of..."
Use: √x = x. 1/2. By the Power Rule (Decrease the power by 1. Multiply by the original power. d/dx √x = d/dx x. 1/2. = 1/2 x.1/2.
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1. Recognize the relationship between the square root and fraction exponents. The rules of mathematics state that the square root of any number A is equal to that number A taken to
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square root of x = x^1/2. therefore derivative = 1/2x^1/2.
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