The nth derivative of 1/x is denoted by $\frac{d^n}{dx^n}(\frac{1}{x})$ and it is equal to (-1)nn!/xn+1. The nth derivative of 1/(ax+b) is denoted by $\frac{d^n}{dx^n}(\frac{1}{ax+b})$ and it is equal to (-1)nann!/(ax+b)n+1. So the n-th derivative formulas of 1/x and logx are given as follows: nth Derivative of 1/x Question: What is the nth derivative of 1/x? … Read more
The nth derivative of sinx and cosx with respect to x are equal to sin(nπ/2 +x) and cos(nπ/2 +x) respectively. In this article, let us learn how to differentiate sinx and cosx with respect to x n-times. The nth order derivative of sinx and cosx are respectively denoted by $\dfrac{d^n}{dx^n}$(sinx) and $\dfrac{d^n}{dx^n}$(cosx). So their formulas … Read more
The derivative of |x| (mod x) is equal to x/|x| where x is non-zero. The function |x| is known as the absolute value of x. So the derivative of absolute value of x is given by $\dfrac{d}{dx}(|x|) = \dfrac{x}{|x|}$, provided that x ≠ 0. Before we prove this formula, let us first recall the definition … Read more
The derivative x root(x) is equal to (3√x)/2. Note x root(x) is denoted by x√x, and its derivative as d/dx (x√x). In this post, let us learn how to differentiate x root(x) using the following methods: The derivative formula of x root(x) is given as follows. $\dfrac{d}{dx}(x\sqrt{x}) = \dfrac{3\sqrt{x}}{2}.$ By Power Rule To find the … Read more
The derivative of fourth foot of x is equal to 1/(4×3/4). Fourth root of x is denoted by ∜x = x1/4, so its derivative formula is given by $\dfrac{d}{dx}$(∜x) = $\dfrac{1}{4x^{3/4}}.$ In this article, we will learn how to differentiate fourth root of x with respect to x by the following methods: By Power Rule … Read more
The chain rule of derivatives is used to find the derivative of a composite function. The rule states that the derivative of a composite function f(g(x)) is equal to f'(g(x)) ⋅ g'(x). In this post, we will learn the statement of the chain rule, its proof, step-by-step method to use this rule along with solve … Read more
The derivative of sec x with respect to x is equal to secx tanx. The secx is the reciprocal of cosx. In this post, we will learn how to find the derivatives of sec x using the following methods: What is the Derivative of Sec x? The derivative of secx with respect to x is … Read more
The derivative (or differentiation) of cot x is equal to -cosec2 x. Let’s learn how to find the derivative of cot x using the following method of derivatives: What is the Derivative of cot x? The derivative of cot x is denoted by the symbol $\frac{d}{dx}$(cot x) or (cot x)$’$ and it is equal to … Read more
The derivative of sin square x is equal to 2sinx cosx (or sin2x). Note that sin2x is the square of sinx. In this article, we will find the derivative of sin2x by the following methods: Derivative of sin2x by Product Rule Step 1: At first, we write sin2x as a product of two copies of … Read more
The derivative of xx (x to the power x) is equal to xx(1+logex). In this post, we will learn the formula for the derivative of xx and how to find it. To calculate the derivative of x to the x, we will use the following methods: Derivative of xx Formula The derivative of xx is … Read more