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: $\dfrac{d}{dx}(x \sin x)$ $=\sin x+x\cos x$. 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 $x^{\dfrac{1}{4}}$. 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 $\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$ $\quad \cdots (I)$ 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: $\dfrac{d}{dx}(f(x))$ $=\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: $\lim\limits_{x \to 0} \dfrac{\log(1+x)}{x}=1$ $\quad \cdots (i)$ 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 $\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ Derivative of sqrt(1+x) using Limit Definition Let $f(x)=\sqrt{1+x}$. … Read more