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Derivative of  $1/\sqrt{1-x^2}$ First Method: At first, we will find the derivative of 1/root(1-$x^2$) by the quotient rule of derivatives. Let us recall the quotient rule of derivatives. If $f$ and $g$ be two functions then the derivative of $f/g$ is given by the following formula: $\dfrac{d}{dx}(f/g)$ $=\dfrac{gf’ -f g’}{g^2}$ $\cdots (\star)$ Here $’$ denotes the … Read more

In this post, we will learn how to find the derivative of various square roots; for example, the derivatives of root(x^2+y^2), x/root(x^2+y^2) and y/root(x^2+y^2).   For more details of square roots, please visit the page Square Root of x: Definition, Symbol, Graph, Properties, Derivative, Integration. Derivative of $\sqrt{x^2+y^2}$ To find the derivative of $\sqrt{x^2+y^2}$ with respect … Read more

Here, we will find the derivative of root x+1/root x with respect to x. In the end, we will also evaluate this derivative at x=1. For more details of square roots, please click on the page Square Root of x: Definition, Symbol, Graph, Properties, Derivative, Integration Root(x)+1/Root(x) Derivative Question: Find the derivative of $\sqrt{x}+\frac{1}{\sqrt{x}}$ Answer: At … Read more

In this section, we will learn how to find To answer the question, let us first know the definition of the derivative. Definition of derivative: Let $f(x)$ be a differentiable function of $x$. From first principle of by definition, the derivative of $f(x)$ is given as follows: $f'(x)=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ Derivative of the Square … Read more