Derivative

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 ${\displaystyle \frac{d}{dx}}(|x|)={\displaystyle \frac{x}{|x|}}$, 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. ${\displaystyle \frac{d}{dx}}(x\sqrt{x})={\displaystyle \frac{3\sqrt{x}}{2}}.$ 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 ${\displaystyle \frac{d}{dx}}$(∜x) = ${\displaystyle \frac{1}{4x^{3/4}}}.$ 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)${}^{\prime }$ 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