promath The limit of tanx/x as x approaches infinity does not exist, that is, limx→∞ tanx/x is undefined. Here we learn to find the limit of tanx/x when x tends to infinity. The formula of the limit of tanx/x when x approaches ∞ is given by limx→∞ tanx/x = undefined. Below theorem will be useful to prove this … Read more
The limit of tanx/x as x approaches 0 is equal to 1, that is, limx→0 tanx/x = 1. Here we learn to find the limit of x/tanx when x tends 0. The formula of the limit of tanx/x when x→0 is given by limx→0 tanx/x = 1. Proof of limit tanx/x = 1 when x→0 First, we prove … Read more
The value of the limit of x/cosx is equal to 0 when x approaches to 0. Here we will learn how to find the limit of x/cosx when x tends 0. The formula of x/cosx limit as x goes to 0 is given below: limx→0 $\dfrac{x}{\cos x}$ = 0. Proof of limit x/cosx is 0 when … Read more
The general solution of dy/dx=ex+y is equal to ex+ e-y= C, and the solution of dy/dx=ex-y is given by ex – ey= C. Here C denotes an arbitrary constant. Let us learn to solve dy/dx = e^(x+y) and dy/dx = e^(x-y), and find their general solutions. General Solution of dy/dx=ex+y Answer: The general solution of … Read more
The general solution of the differential equation dy/dx=sin(x+y) is given by tan(x+y) – sec(x+y) = x +C where C is an arbitrary constant. Here we will learn how to find the solution of dy/dx=sin(x+y). Let us now solve the differential equation dy/dx=sin(x+y) by the substitution method. General Solution of dy/dx=sin(x+y) Question: Find the general solution … Read more
The general solution of the differential equation dy/dx=x/y is given by y2 = x2 + C where C is an integral constant. Here we will learn how to find the solution of dy/dx=x/y. General Solution of dy/dx=x/y Question: Find the general solution of dy/dx=x/y. Answer: The given differential equation is $\dfrac{dy}{dx}=\dfrac{x}{y}$ Separating the variables x … Read more
The derivative of 1/x is equal to -1/x2. In this blog post, we will learn how to find the differentiation of 1/x. Derivative of 1/x Formula: The formula of the derivative of 1/x is given by d/dx(1/x) = -1/x2. Let us find the differentiation of 1/x by first principle which is equal to -1/x2. Derivative … Read more
The derivative of fifth root of x is 1/(5×4/5). In this post, we will learn how to find the derivative of the fifth root x. Here, we will use the power rule of derivatives. Note that the fifth root of x can be written as $\sqrt[5]{x}$ Or, following the rule of indices, the fifth root … Read more
The derivative of 1/lnx is equal to -1/x(lnx)2. In this post, we will learn how to differentiate 1 divided by lnx with respect to x. Let us now find the derivative of 1/lnx using the chain rule and the power rule of derivatives. What is the Derivative of 1/lnx? Answer: The derivative of 1/lnx with … Read more
The derivative of square root of 2x is equal to 1/√(2x). In this post, we will learn how to find the derivative of the square root of 2x. The derivative of the square root of 2x is given by the following formula: $\dfrac{d}{dx}(\sqrt{2x})$ = $\dfrac{1}{\sqrt{2x}}$ Derivative of root 2x by Power Rule To find the … Read more