promath The derivative of x^10 (x to the power 10) is 10×9. In this post, we will find the derivative of x10 by the first principle and the power rule of derivatives. The derivative of x10 is denoted by d/dx (x10), and its formula is given by $\dfrac{d}{dx}(x^{10})=10x^9$. Derivative of x^10 by First Principle The derivative … Read more
The derivative of root secx is equal to (secx tanx)/(2√secx). In this post, we will learn how to find the derivative of root secx by first principles. The formula of the derivative of square root of secx is given as follows: $\dfrac{d}{dx}(\sqrt{\sec x})=\dfrac{\sec x\tan x}{2\sqrt{\sec x}}$. Derivative of square root of secx from first principle … Read more
The derivative of x^5 (x to the power 5) is equal to 5×4. Here, we will learn how to find the derivative of x5 using the power rule and the first principle of derivatives. The derivative of x5 is denoted by d/dx (x5). The derivative formula of x5 is as follows: $\dfrac{d}{dx}(x^5)=5x^4$. Derivative of x^5 … Read more
The derivative of tanx with respect to sinx is equal to sec3x, and it is denoted by d/dsinx (tanx). That is, $\dfrac{d}{d \sin x}(\tan x)=\sec^3 x$. Derivative of tanx w.r.t sinx Question: Find the derivative of tanx w.r.t sinx, that is, Find $\dfrac{d}{d \sin x}(\tan x)$. Answer: Let us put u=tanx and v=sinx. Here we … Read more
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