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
The function log(cos x) denotes the logarithm of the cosine function. Here we will find the derivative of log(cos x) using the first principle of derivatives. The derivative of a function $f(x)$ by the first principle of derivatives is defined to be the following limit: $f'(x)=\dfrac{d}{dx}(f(x))$ $=\lim\limits_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$ $\quad \cdots (i)$ Here the symbol … Read more