To find all the real square roots of – 9/16, first, pay attention to the negative sign in the fraction, and note that negative numbers do not have real square roots. Thus, the answer to this problem is that – 9/16 does not have real square roots. Let’s find out why – 9/16 does not […]

# Author Archives: William Smith

The process of integration is considered the reverse of taking the derivative of a function. We can look at integrals in such a way that the function being integrated is the function in its derivative form while the integral of that function is the original function. That is: begin{align*} int f(x)=F(x)+C end{align*} where begin{align*} dfrac{d}{dx} […]

The “per” in mathematics means “for each” or “for every” and it is used to show a ratio between two quantities or elements. The term per is generally used when we want to compare two quantities, with one as a numerator and the second as a denominator. For example, when we talk about acceleration, we […]

A complex derivative is a derivative that tells us about the rate of change of a complex function. A complex function has two parts, one is a real component and the other is an imaginary component. Complex functions are mathematically represented as: $f(z) = u (x,y) + i v (x,y)$ where $z = x+iy$, and $i=sqrt{-1}$. […]

The derivative of $tan^{-1}x$ is equal to $dfrac{1}{1+x^{2}}$. Mathematically, the formula is written as $dfrac{d}{dx} tan ^{-1} x = (tan^{-1}x)^{‘} = dfrac{1}{1+x^{2}}$. We are basically differentiating the inverse function of a tangent with respect to the variable “$x$”. In this topic, we will study the derivative of the inverse of tan x and its proof […]