The derivative of tan3x is equal to 3sec2 3x. In this post, we will find the derivative of tan3x by the first principle i.e., by the limit definition of derivatives. The first principle of derivatives says that if f(x) is a differentiable function of x, then its derivative is given by the limit below: $\dfrac{d}{dx}(f(x))$$=\lim\limits_{h\to … Read more
The derivative of sin4x is equal to 4cos4x. In this post, we will find the derivative of sin4x by the first principle, that is, by the limit definition of derivatives. The limit definition (i.e., first principle) of derivatives tells us that the derivative of a function f(x) is given by the following limit: $\dfrac{d}{dx}(f(x))$$=\lim\limits_{h\to 0} … Read more
The derivative of cos4(x) is equal to -4cos3(x) sinx. In this post, we will learn how to find the derivative of cos to the power 4 of x. Derivative of cos4x Formula The derivative of $\cos^4(x)$ is denoted by $\dfrac{d}{dx}(\cos^4 x)$ or $(\cos^4 x)’$. The formula of the derivative of cos^4(x) is given below: $\dfrac{d}{dx}(\cos^4 … Read more
The derivative of sin5x is equal to 5sin4x cosx. In this post, we will learn how to differentiate sin5x, that is, sine to the power 5 of x. Derivative of sin5x Formula: The derivative of sin5x is denoted by $\dfrac{d}{dx}(\sin^5 x)$ or $(\sin^5 x)’$. The formula of the derivative of sin5x is given below: $\dfrac{d}{dx}(\sin^5 x)=5\sin^4 … Read more
The derivative of e cube is zero. Note that e cube is written as e3. In this post, we will learn how to find the derivative of e3. Derivative of e3 Formula The formula for the derivative of e3 is 0. This formula is written below. $\dfrac{d}{dx}(e^3)=0$ or $(e^3)’=0$. Here, the prime $’$ denotes the … Read more
The derivative of e square is zero. Note that e square is denoted by e2. In this post, we will learn how to find the derivative of e2, that is, how to differentiate e square. Derivative of e2 Formula The formula for the derivative of e2 is 0. This formula is written below. $\dfrac{d}{dx}(e^2)=0$ or $(e^2)’=0$. … Read more
The derivative of x3 cosx is equal to 3x2cosx – x3sinx. The function x3cosx is the product of two functions x cube and cosx. In this post, we will find the derivative of x3cosx. What is the Derivative of x3cosx? Answer: The derivative of x3cosx is equal to 3x2cosx-x3sinx. Explanation: We will use the product … Read more
The derivative of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of logx. In this post, we will learn how to find the derivative of 1 divided by log x. What is the Derivative of 1/logx? Answer: The derivative of $1/\log x$ is $-\dfrac{1}{x(\log x)^2}$. Explanation: Step 1: Let $z = 1/\log … Read more
The derivative of x^3 is equal to 3x^2. The function x3 denotes the cube of x. In this post, we will find the derivative of x cube by different methods; for example, by the power rule, by the limit definition of derivatives. Derivative of x3 by Power Rule To find the derivative of x cube, … Read more
The derivative of x is equal to 1. The function f(x)=x denotes the identity function on the set of real numbers. In this post, we will find the derivative of x by different methods; for example, by power rule, by the limit definition of derivatives. Derivative of x by Power Rule We will use the … Read more