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# What is the derivative of the square root of x?

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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.

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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.

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## Related Questions

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Find the equation for the tangent line to a curve by finding the derivative of the equation for the curve, then using that equation to find the slope of the tangent line at a given point. Finding the equation for the tangent line requires a knowledge of calculus and the formula for the slope.

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The instantaneous velocity in calculus is the first derivative of a function that expresses distance as a function of time. The instantaneous velocity is also depicted graphically as the slope of the tangent line at a specific point.

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The derivative of 3x is 3. Whenever a mathematical function is defined by a constant multiplied by x, the derivative of the function equals the constant. Thus, the derivative of 2x is 2 and the derivative of 4x is 4.