The derivative of sinx with respect to cosx is denoted by d/dcosx (sinx), and it is equal to -cotx. That is, $\dfrac{d}{d \cos x}(\sin x)=-\cot x$. Let us now learn how to differentiate sin x with respect to cos x. Derivative of sinx w.r.t cosx Question: Find the derivative of sinx w.r.t cosx, that is, … Read more
The derivative of natural log of x is equal to 1/x. As the natural logarithm of x is denoted by lnx, so the derivative formula of natural log of x is given by $\dfrac{d}{dx}{\ln x}=\dfrac{1}{x}$. Find Derivative of Natural log of x Answer: The derivative of natural log of x is 1/x. Explanation: Note the … Read more
The derivative of x^lnx (x to the power lnx) is equal to 2xlnx -1 lnx. Here, ln denotes the natural logarithm, that is, lnx =loge x. In this post, we will learn how to differentiate xlnx. What is the Derivative of xlnx? Answer: Explanation: To find the derivative of xlnx, we will use the logarithmic … Read more
The derivative of e^cosx (e to the power cosx) is equal to -sinx ecosx. In this post, we will find the derivative of ecosx by first principle. The derivative formula of ecosx is given below: $\dfrac{d}{dx}$(ecosx) = -sinx ecosx. Derivative of e^cosx Using First Principle By first principle, the derivative of a function f(x) using … Read more
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