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2. What is the derivative of 2^x? - Socratic

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

   d/dx (2^x) = 2^x * ln2 In order to be able to calculate the derivative of 2^x, you're going to need to use two things the fact that d/dx(e^x) = e^x the chain rule The idea here is that you can use the fact that you know what the derivative of e^x is to try and determine what the derivative of another constant raised to the power of x, in this case equal to 2, is. To do that, you need to write ...

3. How do you find the derivative of 2^x? - Socratic

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

   d/dx2^x=2^xln2 In general, the derivative of an exponential with some constant base is d/dxa^x=a^xlna. A proof of this will be shown. So, d/dx2^x=2^xln2 Proof: Rewrite a^x as e^ln(a^x)=e^(xlna).

4. 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)

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

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

   Answer 2sin(x)cos(x) Explanation You would use the chain rule to solve this. To do that, you'll have to determine what the "outer" function is and what the "inner" function composed in the outer function is. In this case, sin(x) is the inner function that is composed as part of the sin^2(x). To look at it another way, let's denote u=sin(x) so that u^2=sin^2(x). Do you notice how the composite ...

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

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

   The derivative is: 1-tanh^2(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.

7. Limit Definition of Derivative - Calculus - Socratic

   socratic.org/calculus/derivatives/limit-definition-of-derivative

   The derivative of a function f(x) is written f'(x) and describes the rate of change of f(x). It is equal to slope of the line connecting (x,f(x)) and (x+h,f(x+h)) as h approaches 0.

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

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

   f'(x) = 2^(1+2x)ln 2 Given: f(x) = 2^(2x) Derivative rule: (a^u)' = u' a^u ln (a) Let a = 2; " "u = 2x; " "u' = 2 f'(x) = 2* 2^(2x) ln 2 f'(x) = 2^1 * 2^(2x) ln 2 Exponents of the same base are added: f'(x) = 2^(1+2x) ln 2

9. What is the derivative of tan^2 x? - Socratic

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

   #"note "tan^2x=(tanx)^2# #"differentiate using the "color(blue)"chain rule"# #"given "y=f(g(x))" then"# #dy/dx=f'(g(x))xxg'(x)larr" chain rule"#

10. How do you differentiate #y=2^x? - Socratic

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

    The answer is dy/dx[f'(x)]=2^x ln 2. According to chain rule, differentiation of 2^x would be 2^x and the natural log of the base is multiplied to it. You can also take log on both sides and apply log rule to change base for obtaining the answer. The second method would be easier for those who have difficulty in performing chain rule.

11. How do you differentiate y=log x^2? - Socratic

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

    What is the derivative of #f(x)=(log_6(x))^2# ? See all questions in Differentiating Logarithmic Functions without Base e Impact of this question