The derivative of 1/xn (1 by x power n) is equal to -n/xn+1. Here we learn how to find the derivative of 1 divided by x to the n. The derivative formula of 1/x^n is given by $\dfrac{d}{dx} \big( \dfrac{1}{x^n}\big) = -\dfrac{n}{x^{n+1}}$. Derivative of 1/xn Answer: The derivative of 1/xn is equal to -n/xn+1. Explanation: … Read more
The derivative of ln(lnx) is equal to 1/xln(x) and it is denoted by d/dx (x lnx). So the derivative formula of ln(lnx) is given by $\dfrac{d}{dx}\big(\ln(\ln x) \big) = \dfrac{1}{x \ln x}$. Derivative of ln(lnx) by Chain Rule Answer: The derivative of ln(lnx) is $\dfrac{1}{x \ln x}$. Explanation: Let z=ln x. Differentiating, $\dfrac{dz}{dx}=\dfrac{1}{x}$. Now, $\dfrac{d}{dx}\big(\ln(\ln … Read more
The derivative of 4/x is equal to -4/x2. In this post, we will find the derivative of 4 divided by x by the power rule. The derivative of 4/x is denoted by d/dx(4/x), and its formula is given by $\dfrac{d}{dx}(\dfrac{4}{x})= – \dfrac{4}{x^2}$. Derivative of 4/x Question: Find the Derivative of 4/x. Answer: We can express … Read more
The derivative of 3/x is equal to -3/x2. The derivative formula of 3/x (3 divided by x) is given by as follows: $\dfrac{d}{dx}(\dfrac{3}{x})= – \dfrac{3}{x^2}$. Derivative of 3/x Question: What is the Derivative of 3/x? Answer: As 3/x can be expressed as 3x-1, applying the power rule, the derivative of 3/x is equal to -3/x². … Read more
The derivative of 2/x is equal to -2/x2. Here, we will learn how to find the derivative of 2 divided by x. The derivative formula of 2/x is given by $\dfrac{d}{dx}(\dfrac{2}{x})= – \dfrac{2}{x^2}$. Derivative of 2/x Question: Find the Derivative of 2/x. Answer: We can express 2/x as 2x-1. So by the power rule, the … Read more
The derivative of ln(1/x) is equal to -1/x, where ln denotes the logarithm with base e, that is, ln(x)=logex. In this post, we will find the derivative of ln(1/x). Note that ln(1/x) is the natural logarithm of 1/x. Its derivative formula is given below: $\dfrac{d}{dx}\big( \ln (\dfrac{1}{x}) \big)=-\dfrac{1}{x}$. Derivative of ln(1/x) by Chain Rule Let … Read more
The derivative of root 1-x^2 is equal to -x/√(1-x2). Here we differentiate square root of 1-x2 by chain rule and implicit differentiation method. Note that $\dfrac{d}{dx} \Big( \sqrt{1-x^2}\Big)=-\dfrac{x}{\sqrt{1-x^2}}$. Let us now differentiate root 1-x2. Derivative of root 1-x2 by Chain Rule Question: Find the derivative of square root 1-x2. Answer: Let us put z = … Read more
The derivative of sec2x by first principle is equal to 2sec2x tan2x. In this post, we will find the derivative of sec2x by first principle. The first principle rule of derivatives states that the derivative of f(x) is given by the limit f$’$(x) = limh→0 $\dfrac{f(x+h)-f(x)}{h}$. Let us now find the differentiation of sec2x by … Read more
The derivative of x^logx (x to the power logx) is equal to 2 logx xlogx-1. Here we find the differentiation of xlogx by using the product rule of derivatives together with logarithmic differentiation. The product rule of derivatives states the following: $\dfrac{d}{dx}$(f(x)g(x)) = f(x) $\dfrac{d}{dx}$(g(x)) + g(x) $\dfrac{d}{dx}$(f(x)) …(I) Find the Derivative of xlogx Answer: … Read more
The derivative of cos cube x (cos^3x) is equal to -3cos2x sinx. In this post, we will find the derivative of cos cube x using the chain rule. The derivative formula of cos3x is given as follows: d/dx (cos3x) = -3cos2x sinx. Derivative of Cos^3x The derivative of cos3x is -3cos2x sinx. Explanation: As cos3x … Read more