promath 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 value of log 16 base 4 is equal to 2, that is, log416 = 2. The logarithm of 16 to the base is expressed as log416, and its formula is given by $\boxed{\log_4 16 =2}$. From the definition, we know that x = logab if and only if ax=b. Therefore, if the x 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 value of natural log of e is equal to 1. The natural log of e is denoted by ln(e), and it is equal to logee. The formula of natural log of e is given by ln(e) =1. Value of Natural log of e Question: What is natural log of e? Answer: The natural log … Read more
The natural log of x is the logarithm of x with base e, and it is denoted by ln(x). That is, logex = lnx. The integral of natural log of x is equal to ∫ln(x) dx = xln(x) -x+C, where C is a constant. Here, we will learn how to find the integration of natural … Read more
The general solution of the differential equation dy/dx+ytanx = secx is equal to ysecx =tanx +C where C is a constant. This equation is an example of a first order linear ordinary differential equation. Solve dy/dx+ytanx = secx Question: Solve the differential equation $\dfrac{dy}{dx}$+ytanx = secx. Solution: The given equation has the form $\dfrac{dy}{dx}+P(x)=Q(x)$, a … Read more
The value of log 81 base 3 is equal to 4. As log 81 base 3 is written as log381, we have that log381 =4. In this post, we will learn how to find the logarithm of 81 with base 3. The formula of the logarithm of 81 with base 3 is given as follows: … Read more
The value of log 81 with base 27 is equal to 4/3. The logarithm of 81 with base 27 is written as log2781, so the formula of log81 base 17 is given by log2781 = 4/3. Value of log 81 base 27 Answer: The value of log 81 base 27 is equal to 4/3, that … Read more
The general solution of the differential equation (x+y+1)dy/dx=1 is equal to x= -(y+2)+Cey where C denotes an arbitrary constant. Here we will learn how to solve the differential equation (x+y+1)dy/dx=1. Solve (x+y+1)dy/dx=1 Question: What is the solution of (x+y+1)$\dfrac{dy}{dx}$=1? Answer: Let us put x+y+1 = v. Differentiating w.r.t x, we get that $1+\dfrac{dy}{dx}=\dfrac{dv}{dx}$ ⇒ $\dfrac{dy}{dx}=\dfrac{dv}{dx}-1$ … Read more
The value of log 2 with base 8 is equal to 1/3. The logarithm of 2 with base 8 is written as log82, so the formula of log2 base 8 is given by log82 = 1/3. Value of log 2 base 8 Answer: The value of log 2 base 8 is equal to 1/3, that … Read more