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2. What is the derivative of #tanh(x)#? - Socratic

   socratic.org/questions/what-is-the-derivative-of-tanh-x

   The derivative is: 1 −tanh2(x) Hyperbolic functions work in the same way as the "normal" trigonometric "cousins" but instead of referring to a unit circle (for sin,cos and tan) they refer to a set of hyperbolae. (Picture source: Physicsforums.com) You can write: tanh(x) = ex −e−x ex +e−x. It is now possible to derive using the rule of ...

3. What is the derivative of #f(x)=tan^-1(x)# - Socratic

   socratic.org/questions/what-is-the-derivative-of-f-x-tan-1-x

   I think he originally intended to do this: dy dx = 1 sec2y. sec2y = 1 + tan2y. tan2y = x → sec2y = 1 +x2. ⇒ dy dx = 1 1 + x2. Answer link. I seem to recall my professor forgetting how to deriving this. This is what I showed him: y = arctanx tany = x sec^2y (dy)/ (dx) = 1 (dy)/ (dx) = 1/ (sec^2y) Since tany = x/1 and sqrt (1^2 + x^2) = sqrt ...

4. How do you take the derivative of #Tan^-1 (y/x)#? - Socratic

   socratic.org/questions/how-do-you-take-the-derivative-of-tan-1-y-x

   Jun 7, 2015. I'm assuming you are thinking of this as being a function of two independent variables x and y: z = tan−1(y x). The answers are ∂z ∂x = − y x2 +y2 and ∂z ∂y = x x2 + y2. Both of these facts can be derived with the Chain Rule, the Power Rule, and the fact that y x = yx−1 as follows:

5. What is the derivative of #tan(xy)#? - Socratic

   socratic.org/questions/what-is-the-derivative-of-tan-xy

   Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer

6. Derivative of Tan | Differentiation & Formula - Lesson -...

   study.com/academy/lesson/how-to-take-the-derivative-of-tan-x.html

   The differentiation of tan (x) is a vital step towards solving math and physics problems. To review this differentiation, the derivative of tan (x) can be written as: d d x tan (x) = d d x (sin (x ...

7. What is the derivative of inverse tangent of 2x? | Socratic

   socratic.org/questions/what-is-the-derivative-of-inverse-tangent-of-2x

   What is the derivative of inverse tangent of 2x? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 2 Answers

8. What is the derivative of #y=tan(x)# - Socratic

   socratic.org/questions/what-is-the-derivative-of-y-tan-x

   The derivative of tanx is sec^2x. To see why, you'll need to know a few results. First, you need to know that the derivative of sinx is cosx. Here's a proof of that result from first principles: Once you know this, it also implies that the derivative of cosx is -sinx (which you'll also need later). You need to know one more thing, which is the Quotient Rule for differentiation: Once all those ...

9. What is the antiderivative of #tan(x)#? - Socratic

   socratic.org/questions/what-is-the-antiderivative-of-tan-x

   Recall: int{g'(x)}/{g(x)}dx=ln|g(x)|+C (You can verify this by substitution u=g(x).) Now, let us look at the posted antiderivative. By the trig identity tan x={sin x}/{cos x}, int tan x dx=int{sin x}/{cos x}dx by rewriting it a bit further to fit the form above, =-int{-sin x}/{cos x}dx by the formula above, =-ln|cos x|+C or by rln x=lnx^r, =ln|cos x|^{-1}+C=ln|sec x|+C I hope that this was ...

10. How do you take the derivative of tan^-1 2x? - Socratic

    socratic.org/questions/how-do-you-take-the-derivative-of-tan-1-2x

    Use the derivative of tan^-1 and the chain rule. The derivative of tan^-1x is 1/ (1+x^2) (for "why", see note below) So, applying the chain rule, we get: d/dx (tan^-1u) = 1/ (1+u^2)* (du)/dx In this question u = 2x, so we get: d/dx (tan^-1 2x) = 1/ (1+ (2x)^2)*d/dx (2x) = 2/ (1+4x^2) Note If y = tan^-1x, then tany = x Differentiating implicitly ...

11. How do you take the derivative of #tan^-1(x^2)#? - Socratic

    socratic.org/questions/how-do-you-take-the-derivative-of-tan-1-x-2

    Remember that you have. sec2x = 1 + tan2x. which means that you get. dy dx = 2x 1 + tan2y. Finally, replace tan2y with x2 to get. dy dx = 2x 1 +x4. Answer link. y^' = (2x)/ (1 + x^4) You can differentiate a function y = tan^ (-1) (x^2) by using implicit differentiation. So, if you have a function y = tan^ (-1) (x^2), then you know that you can ...