promath The derivative of lnx^2 is equal to 2/x. The natural logarithm of x2 is denoted by ln(x2), and its derivative formula is given by $\dfrac{d}{dx}(\ln x^2)=\dfrac{2}{x}.$ That is, the differentiation of ln(x2) is 2/x. Derivative of ln(x2) by Chain Rule Answer: The derivative of ln(x2) is 2/x. Explanation: To find the derivative of ln(x2) by … Read more
The derivative of ln(x+1) is equal to 1/(x+1). Ln(x+1) denotes the natural logarithm of x+1, that is, ln(x+1) = loge(x+1). Here we will find the derivative of ln(x+1) using the following methods: The derivative of ln(x+1) is denoted by d/dx {ln(x+1)} and its formula is given by $\dfrac{d}{dx} \Big(\ln (x+1) \Big)=\dfrac{1}{x+1}.$ Derivative of ln(x+1) by … Read more
The derivative of lnx is equal to 1/x. Ln(x) denotes the natural logarithm of x, that is, lnx= logex. Here we will find the derivative of ln(x) using the limit definition and chain rule of differentiation. Note that lnx= logex. The derivative of lnx is denoted by d/dx(lnx), and its formula is given as follows: … Read more
The derivative of ln u is equal to 1/u du/dx, and this is the derivative of ln(u) with respect to x. Here we differentiate the natural logarithm of u with respect to x. Recall that, ln u = logeu. Derivative of ln(u) If u is a function of x, then the derivative of ln u … Read more
The derivative of ln3x is equal to 1/x, where ln denotes the natural logarithm. Here we will find the derivative of ln(3x). The ln3x differentiation formula is given below: $\dfrac{d}{dx}(\ln 3x)=\dfrac{1}{x}$. ln(3x) Derivative Question: Find the derivative of ln3x. Solution: By the logarithm rule for products, ln 3x = ln3 + lnx. So, $\dfrac{d}{dx}(\ln 3x)$ … Read more
The derivative of tan root x is equal to (sec2√x)/2√x. By the chain rule of differentiation, the derivative formula of tan(√x) with respect to x is given as follows: $\dfrac{d}{dx}(\tan \sqrt{x})=\dfrac{\sec^2 \sqrt{x}}{2\sqrt{x}}$. Derivative of tan(√x) by Chain Rule Answer: The derivative of tan√x is (sec2√x)/2√x. Explanation: Let us put z = √x. Differentiating both sides … Read more
The derivative of cos root x is equal to (-sin√x)/2√x. Here we will find the derivative of cos√x by the chain rule of derivatives. The differentiation of cos(√x) with respect to x is given by $\dfrac{d}{dx}(\cos \sqrt{x})=-\dfrac{\sin \sqrt{x}}{2\sqrt{x}}$. Let us now find the derivative of cos root x using the chain rule of differentiation. Derivative … Read more
The general solution of the differential equation dy/dx = xy2 is given by y=-2/(x2+2K) where K is an arbitrary constant. Here we will learn how to find the general solution of the differential equation. Set C=2K. Answer: the solution of $\dfrac{dy}{dx}=xy^2$ is given by y = $-\dfrac{2}{x^2+C}$. Solve dy/dx=xy2 Given $\dfrac{dy}{dx}=xy^2$ To solve it, we … Read more
The 1-sinx formula is given by 1-sinx= [cos(x/2) -sin(x/2)]2. The 1 plus sinx idenity is given as follows: $1+\sin x =(\cos \frac{x}{2}+\sin \frac{x}{2})^2$. Let us now find the formula of 1-sinx and 1+sinx. Formula of 1-sinx Answer: 1-sinx= $(\cos \frac{x}{2}-\sin \frac{x}{2})^2$. Explanation: To find the formula of 1-sinx, we will use the following two trigonometric … Read more
The 1-cosx identity is given by 1-cosx= 2sin2(x/2). 1 minus cosx is a trigonometric expression and its formula is given below: $1-\cos x =2 \sin^2 (\frac{x}{2})$. Let us now find the formula of 1-cosx in terms of sin. 1-cosx Formula in Terms of Sin Answer: 1-cosx formula in terms of sin is equal to 1-cosx= … Read more