coolbeans33 said:I know that the derivative of the sqrt x = .5x^-1/2
I think that x^-1 equals 1/x right?
so what does .5x^-1/2 equal? I am kind of confused!
is it 1/4x?
Chris L T521 said:Since there are no parenthesis, then $.5x^{-1/2} = .5\cdot x^{-1/2}= \dfrac{.5}{x^{1/2}} = \dfrac{1}{2x^{1/2}}$.
I hope this clarifies things!
(1/2)x^(-1/2) is an algebraic expression that represents a function. It cannot be simplified further unless the value of x is known. In general, (1/2)x^(-1/2) is equal to 1/√x.
As mentioned before, (1/2)x^(-1/2) cannot be simplified unless the value of x is known. However, it can be rewritten as 1/√x which is a more simplified form.
The domain of a function refers to all the possible values of x for which the function is defined. In the case of (1/2)x^(-1/2), x can take on any positive value, since the square root of a negative number is not defined in real numbers. Therefore, the domain is all positive real numbers.
The range of a function refers to all the possible values of y (or f(x)) that the function can output. In the case of (1/2)x^(-1/2), the range is also all positive real numbers. This is because as x approaches 0 from the positive side, the value of the function approaches infinity.
(1/2)x^(-1/2) is commonly used in physics and engineering to represent inverse square laws, such as the law of gravitation and the law of Coulomb's inverse square. It is also used in finance to calculate compound interest rates and in statistics to represent probability density functions.