The derivative of e^sinx is equal to cosx esinx. In this post, we will find the derivative of esinx by first principle. The esinx derivative formula is given as follows: $\dfrac{d}{dx}$(esinx) = cosx esinx. Derivative of e^sinx Using First Principle The derivative of f(x) using the first principle is given by the following limit formula: … Read more
The partial derivative of xy with respect to x is equal to y and the partial derivative of xy with respect to y is equal to x. Their formula is given below: Partial Derivative of xy with respect to x Let us will find the partial derivative of xy using the definition. Let f(x, y) … Read more
The derivative of x/y with respect to x is equal to (-x dy/dx + y)/y2. Here, we will learn how to differentiate x/y with respect to x. Derivative of x/y with respect to x Question: Differentiate x/y with respect to x. Solution: Note that $\dfrac{x}{y}$ is a product of two functions $x$ and $\dfrac{1}{y}$. So … Read more
The derivative of the mod cosx is equal to (- sinx cosx)/|cosx|. Here let us learn how to differentiate mod cosx, that is, how to find d/dx(|cosx|). The derivative formula of mod cosx is given as follows. $\boxed{\dfrac{d}{dx}(|\cos x|)=\dfrac{-\sin x \cos x}{|\cos x|}}$, provided that cosx is non-zero. The following formula is very useful to … Read more
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