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.
Know MoreThe 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.
Learn MoreThe antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be solved by using the integration technique known as substitution.
Full Answer >To find the square root of 101, the square root of the number needs to be divided into several different numbers; three should be placed on top of the square root symbol nine should be put underneath the 10 part of the number and subtracted. The last part of the number, one, should be brought down to line up with the other one that was the result of the subtraction. After using the algorithm, the square root of 101 will work out to be 10.0498756211209.
Full Answer >The derivative of y = arctan(6x) is 6/(1 + 36 x^2). To arrive at this answer, it is simply a matter of using the formula given for finding the derivative of the inverse tangent function. The formula is that for arctan (u) the derivative is du/(1 + u^2).
Full Answer >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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