Derivative

The derivative of xsin x is sin x+x cos x. In this post, we will find the differentiation of x sin x using the first principle of derivatives. The derivative formula of xsin x is given below: ${\displaystyle \frac{d}{dx}}(x\sin x)$ $=\sin x+x\cos x$. We will now prove the above formula. Derivative of xsin x by … Read more

Note that n-th root can be written as raised to the power 1/n}. The derivative of n-th root of x is 1/n x^{1/n -1}. In this post, we will find the derivative of n-th root of x. Remark: The nth root of x is written as Derivative of nth root of x Using the rule … Read more

The derivative of fourth root of x is 1/(4 x^{3/4}). In this post, we will find the derivative of the fourth root of x using the power rule of derivatives. Note that fourth root of x can be written as Alternatively, one can write it as $x^{{\displaystyle \frac{1}{4}}}$. Derivative of Fourth Root of x To find … Read more

The derivative of x root x is 3 root(x)/2. In this post, we will find the derivative of x root(x) from first principle. This principle says that the derivative of f(x) is ${\displaystyle \frac{d}{dx}}(f(x))$ $=\underset{h\to 0}{lim}{\displaystyle \frac{f(x+h)-f(x)}{h}}$ $\cdots (I)$ Derivative of x root x by First Principle Let $f(x)=x\sqrt{x}$ in the above formula (I). So … Read more

  The derivative of e^4x with respect to x is 4e^4x. In this post, we will evaluate the derivative of e to the power 4x from first principle.  Derivative of e^4x by first principle Let f(x) be a function in one variable x. The derivative of f(x) from first principle is given by the following … Read more

Answer: The derivative of e^2x by first principle is equal to 2e2x. In this article, we will find the derivative of e to the power 2x using the first principle. Recall that for a function f(x) in one variable x, the derivative of f(x) from first principle is given by the limit below: ${\displaystyle \frac{d}{dx}}(f(x))$ $=\lim\limits_{h … Read more

The derivative of log3x is 1/x. In this post, we will find the derivative of log 3x by first principle. To do so, we will use the following limit formula on logarithm functions: $\underset{x\to 0}{lim}{\displaystyle \frac{\log (1+x)}{x}}=1$ $\cdots (i)$ Derivative of log 3x from First Principle The first principle of derivatives says that the … Read more

Derivative of root x: The square root of x is a very important function in Mathematics. In this post, we will find the derivative of the square root of x using the first principle of derivatives and by the power rule of derivatives. At first, we find the derivative of root x by limit definition, … Read more

The derivative of e3x is 3e3x. The function e^3x is an exponential function with an exponent 3x. In this note, we will find the derivative of e to the power 3x by the first principle of derivatives and by the chain rule of derivatives. Derivative of e^3x using first principle As we know that the derivative … Read more

Note that the square root of 1+x can be written as (1+x)1/2. In this post, we will find the derivative of the square root of 1+x by the first principle of derivatives. Using this principle, the derivative of a function f(x) is ${\displaystyle \frac{d}{dx}}(f(x))$ $=\underset{h\to 0}{lim}{\displaystyle \frac{f(x+h)-f(x)}{h}}$ Derivative of sqrt(1+x) using Limit Definition Let $f(x)=\sqrt{1+x}$. … Read more