promath The derivative of tan^2x is 2tanx sec2x. Here we will find the derivative of tan square x by the first principle of derivatives. The first principle says that the derivative of a function f(x) is given by the following limit formula: $\dfrac{d}{dx}(f(x))$ = limh→0 $\dfrac{f(x+h)-f(x)}{h}$ …(I) Let us now learn how to differentiate tan square … Read more
The derivative of tan square x is equal to 2tanx sec2x. Here we find the derivative of tan2x by the chain and product rule. The derivative formula of tan square x is given below: $\dfrac{d}{dx}(\tan^2 x)=2 \tan x \sec^2x$. What is the derivative of tan square x? Let us find the derivative of tan2x by … Read more
The derivative of sinx cosx is equal to cos2x. Here we learn to find the differentiation of sinx cosx by the product rule. The derivative formula of the product sinx cosx is given as follows: $\dfrac{d}{dx}$(sinx cosx) = cos2x. Find the Derivative of sinx cosx We know that sin2x = 2 sinx cosx. Thus, it … Read more
The derivative of tan2x is equal to 2sec22x. Here we will prove this by the first principle. In this post, we will learn how to differentiate tan2x with respect to x. The derivative of tan2x formula is given by $\dfrac{d}{dx}(\tan 2x)$ = 2sec22x. Differentiate tan2x Using First Principle To differentiate tan2x using the first principle, … Read more
The derivative of sin cube x is equal to 3sin2x cosx. Here we learn how to differentiate sin^3x. The sin^3x derivative formula is d/dx(sin3x) = 3sin2x cosx. The derivative of sine cube x is denoted by d/dx(sin3x) 0r (sin3x)$’$ and it is equal to Derivative of sin3x by Chain Rule To find the derivative of … Read more
The integration of sin cube x is equal to -cosx + cos3x/3+C where C denotes an integral constant. In this post, we will learn how to integrate sin^3x. Sine cube x integration formula: The integration formula of sin3x is given by What is the integral of sin^3x Answer: The integral of sin^3x is equal to … Read more
The limit of (cosx-1)/x as x approaches 0 is equal to 0. Here, we will learn to find the limit of (cos(x)-1)/x when x→0. The limit formula of (cosx-1)/x as x tends to 0 is given by limx→0 $\dfrac{\cos x -1}{x}$ = 0. Proof of Limit of (cosx-1)/x as x approaches 0 Prove that limx→0 … Read more
The derivative of cos3x is equal to -3sin3x. Here we learn how to differentiate cos3x and find the derivative of cos3x by first principle. Derivative Formula of cos3x The formula of the derivative of cos3x is given by d(cos3x)/dx = -3sin3x. That is, the derivative of cos3x is equal to the negative of three times … Read more
The integral of sinxcosx is equal to -(cos2x)/4+C or, (sin2x)/2+C where C is an integration constant. In this post, we will learn how to integrate sinx cosx. The integration formula of sinxcosx is give as follows: Find the integration of sinx cosx Answer: The integration of sinx cosx is (sin2x)/2+C. proof: There are three methods … Read more
The limit of sin2x/sin3x when x approaches 0 is equal to 2/3, that is, limx→0 sin2x/sin3x = 2/3. The limit of sin3x/sin2x when x approaches 0 is equal to 3/2, that is, limx→0 sin3x/sin2x = 3/2. The following formula will be useful to compute the above limits: limx→0 sinx/x = 1 …(∗) Limit of sin2x/sin3x … Read more