What Is the Derivative of the Square Root of X?

What Is the Derivative of the Square Root of X?

What Is the Derivative of the Square Root of X?

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.