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2. How do find the derivative of # y = cos^2(x)#? - Socratic

   socratic.org/questions/how-do-find-the-derivative-of-y-cos-2-x

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

3. How do you differentiate #y = cos^2 (x^2)#? - Socratic

   socratic.org/questions/how-do-you-differentiate-y-cos-2-x-2

   1 Answer. Anees. Apr 16, 2015. y' = − 4xcos(x2)(sinx2) Solution. y = cos2(x2)) Differentiating both sides with respect to 'x'. y' = d dx cos2(x2))

4. What is the derivative of #ln(cos^2(x))#? - Socratic

   socratic.org/questions/what-is-the-derivative-of-ln-cos-2-x

   f(x) = ln(cos^2x) = ln((cosx)^2) = 2ln(cosx) f'(x) = 2 1/cosx (-sinx) " " (Chain rule: d/dx(lnu) = 1/u (du)/dx) = -2tanx

5. How do you find the antiderivative of #cos^2 (x)#? - Socratic

   socratic.org/questions/how-do-you-find-the-antiderivative-of-cos-2-x-1

   Thus: ∫cos2(x)dx = 1 2 ∫cos(2x) + 1dx. We can now split this up and find the antiderivative. = 1 2 ∫cos(2x)dx + 1 2 ∫1dx. = 1 4 ∫2cos(2x)dx + 1 2x. = 1 4 sin(2x) + 1 2 x + C. Answer link. 1/4sin (2x)+1/2x+C The trick to finding this integral is using an identity--here, specifically, the cosine double-angle identity.

6. How do you find the derivative of #y=cos(x^2)# - Socratic

   socratic.org/questions/how-do-you-find-the-derivative-of-y-cos-x-2-1

   The chain rule states: d dx [f (g(x))] = d d[g(x)] [f (x)] ⋅ d dx [g(x)] In other words, just treat x2 like a whole variable, differentiate the outside function first, then multiply by the derivative of x2. We know that the derivative of cosu is −sinu, where u is anything - in this case it is x2. And the derivative of x2 is 2x.

7. What is the derivative of #sin^2(x) * cos^2(x)#? - Socratic

   socratic.org/questions/what-is-the-derivative-of-sin-2-x-cos-2-x-4

   Starting with sin^2 (x) and using the chain rule to take its derivative, we have: 2sin (x)*cos (x) Now, by the product rule, we multiply this by our second term, cos^2 (x), so the left side of the derivative is 2sin (x)*cos (x)*cos^2 (x) or 2cos^3 (x)sin (x) Now for the right side, we use the chain rule to take the derivative of cos^2 (x): 2cos ...

8. What is the derivative of cosx^2? - Socratic

   socratic.org/questions/what-is-the-derivative-of-cosx-2

   How do you find the 50th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x^2)# ? See all questions in Derivative Rules for y=cos(x) and y=tan(x)

9. How do you differentiate #cos(x^2)#? - Socratic

   socratic.org/questions/how-do-you-differentiate-cos-x-2

   How do you compute the 200th derivative of #f(x)=sin(2x)#? How do you find the derivative of #sin(x^2+1)#? See all questions in Differentiating sin(x) from First Principles

10. What is the derivative of #cos^-1(x)#? - Socratic

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

    d/dxcos^(-1)(x) = -1/sqrt(1 -x^2) When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you can use the chain rule. Let y=cos^(-1)(x) <=> cosy=x Differentiate Implicitly ...

11. How do you find the derivative of #(cos x)# using the limit ... -...

    socratic.org/questions/how-do-you-find-the-derivative-of-cos-x-using-the-limit...

    See the explanation section below. We'll need the following facts: From trigonometry: cos(A+B) = cosAcosB-sinAsinB Fundamental trigonometric limits: lim_(theta rarr0 ...