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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 derivative of tan(2x) is equal to two times the secant squared of two times x. Using mathematical notation, the equation is written as d/dx tan(2x) = 2sec^2(2x).

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A person can consider a differential equation by determining an initial condition, as a differential equation is an equation that gives the derivative of an unknown function in terms of the function and the independent variable. A differential equation is considered differently depending on whether it is ordinary or partial and linear or non-linear.