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 more in CalculusThe derivative of x is 1. A derivative of a function in terms of x can be thought of as the rate of change of the function at a value of x. In the case of f(x) = x, the rate of change is 1 at all values of x.
Full Answer >The multivariable chain rule is a formula in calculus used to find the derivative of the composition of multiple functions. In the multivariable chain rule, a function expressed as y(w(x)) can be differentiated using the equation dy/dx = (dy/dw)*(dw/dx), where d indicates the derivative of the variable.
Full Answer >The derivative of secant is equal to the tangent of x times the secant of x. Expressed in mathematical terms, the equation reads as d/dx secant(x) = tan(x)sec(x).
Full Answer >In calculus, critical points or stationary points are any values of differentiable functions of complex or real variables whose derivative is 0, f(x0) = 0. In a differentiable function that has several real variables, critical points are values in the domain where the partial derivatives are 0. The values of critical points are known as critical values.
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