If f(x) is a function of the real variable x, then its derivative by the first principle of the derivative is given by $f'(x)=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ $\quad \cdots (i)$ Here $’$ denotes the derivative. In this post, we will find the derivative of \log(\sin x) by the first principle of derivatives. Derivative of log(sinx) … Read more
The derivative of square root of cosx is equal to (-sin x)/(2 root(cos x)).In this post, we will learn how to find the derivative of root cosx by first principle, that is, by the limit definition. The first principle of derivative is defined as follows: Let $f(x)$ be a differentiable function of $x$. The derivative … Read more
This page will discuss the continuity and differentiability of the absolute value of $x-a$, that is, of the function $|x-a|$, at the point $x=a$. Note that the function $|x-a|$ is defined as follows: $|x-a| = x-a$ if $x\geq a$ $=-(x-a)$ if $x<a$ Continuity of |x-a| at x=a Let us now discuss the continuity of the … Read more
The derivative of $\tan x$ is $\sec^2 x$, that is, $\dfrac{d}{dx}(\tan x)=\sec^2 x$. In this post, we will learn how to find the derivative of \tan x by the product rule of derivatives as well as the quotient and chain rule of derivatives. At first, we will recall the rules. Let $f(x)$ and $g(x)$ … Read more
The integration of root x is equal to 2/3 x3/2+C. In this post, we will calculate the integration of the square root of x. Note that the square root of x is an algebraic function. We will use the following power rule of derivatives: $\int x^n dx = \dfrac{x^{n+1}}{n+1}+c$ $ \cdots (i)$ where $c$ is … Read more
Here we will learn various types of calculus problems. For example, Limit (Link for Limits) Limit: definition, properties, and formulas Proofs of all limit formulas Solved Problems of Basic Limits Solved Problems of Trigonometric Limits Solved Problems of Exponential Limits Limits of Some Special Functions (to be updated) Intermediate Forms (to be updated) L’Hopital’s Rule with Applications (to … Read more