The derivative of the square root of x is onehalf times one divided by the square root of x. The square root of x is equal to x to the power of onehalf.
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 onehalf. Onehalf minus one is negative onehalf, so the derivative is onehalf times x to the power of negative onehalf. X to the negative n equals one divided by x to the n, so the derivative is onehalf times one divided by x to the power of onehalf. Since x to the power of onehalf is the square root of x, the final result is onehalf times one divided by the square root of x.
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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The derivative of square root of x is expressed D[sqrt(x)] = 1/(2*s...
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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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