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About Differential Calculus AI

CalculusPop differential calculus AI solver that can handle a variety of differentiation problems. It can solve equations using first principles and the general rule for differentiation of functions like y = ax^n, sine, cosine, exponential functions, and logarithmic functions.

The calculus AI also covers methods of differentiation, including the differentiation of products and quotients, functions of functions, and implicit functions. It can handle applications of differentiation such as rates of change, velocity, acceleration, turning points, maximum and minimum values, points of inflexion, tangents and normals, and small changes in functions.

The AI can also differentiate parametric equations, common parametric equations, and hyperbolic functions. Moreso, it covers logarithmic differentiation and further logarithmic functions. With its ability to solve a wide range of differentiation problems, this AI is a valuable tool for students and professionals working in calculus and related fields.

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3x^2 \cdot \sin (2x) as 3x^2* sin (2x) 

1. \frac{d}{dx}(5x^2 + 3x - 7) as 5x^2 + 3x - 7

2. \frac{d}{dx}(e^{2x} + \sin(x)) as e^(2x) + sin(x)

3. \frac{d}{dx}(4x \cdot \cos(x)) as x * cos(x)

4. \frac{d}{dx}\left(\frac{3x^2}{x+1}\right) as 3x^2/ (x+1)

5. \frac{d}{dx}(\ln(2x)) as ln(2x)

6. \frac{d}{dx}(10x \cdot \tan(x)) as 10x * tan(x)

7. \frac{d}{dx}\left(\frac{x^2}{\sin(x)}\right) as x^2/sin(x)

8. \frac{d}{dx}(e^{3x}\cos(x)) as e^(3x)\cos(x)

9. \frac{d}{dx}(x^3 \cdot \ln(x)) as  x^3 * ln(x)

10. \frac{d}{dx}\left(\frac{2x+1}{x^2-3}\right) as (2x+1)/(x^2-3)

11. \frac{d}{dx}(5\sin(x) + 2\cos(x)) as 5*sin(x) + 2*cos(x)

12. \frac{d}{dx}(e^{4x} \cdot \tan(x)) as e^(4x) * tan(x)

13. \frac{d}{dx}\left(\frac{x^3}{\cos(x)}\right) as (x^3)/(cos(x))

14. \frac{d}{dx}(\ln(4x^2)) as ln(4x^2)

15. \frac{d}{dx}(7x^2 \cdot \sin(x)) as 7x^2 * sin(x)

16. \frac{d}{dx}\left(\frac{x}{e^x}\right) as  x/e^(x)

17. \frac{d}{dx}(3\cos(x) - 8\sin(x)) as 3*cos(x) - 8*sin(x)

18. \frac{d}{dx}(e^{x^2}\cdot \csc(x)) as e^(x^2)*csc(x)

19. \frac{d}{dx}(x^4 \cdot \log(x)) as  x^4 * log(x)

20. \frac{d}{dx}\left(\frac{3x-2}{x^3+1}\right) as (3x-2)/(x^3+1)

21.  x = \sin(t), y = \cos(t) as x = sin(t), y = cos(t)

22. y^2 - \ln(x) = 0 as y^2 - In(x)

23. \frac{d}{dx}\left( \ln(2x) \right) as ln(2x)

24. \frac{d}{dx}\left( \sinh(x) \right) as sinh(x)

25. \frac{d}{dx}\left( \cosh(x) \right) as cosh(x) 

26. \frac{d}{dx}\left( \tanh(x) \right) as tanh(x)

27. \frac{d}{dx}\left( \tanh(ax^2 + bx + c) \right) as tanh(ax^2 + bx + c)

28. \frac{d}{dx}\left( e^{\cos(x)} \right) as e^(cos(x))

29. \frac{d}{dx}\left( \log_a(x) \right) as log_a(x) 

30. \frac{d}{dx}\left( \sin^{-1}(x) \right) as sin^(-1)(x)

1. Differentiation from first principles
2. Differentiation of y = ax n by the general
   rule
3. Differentiation of sine and cosine functions
4. Differentiation of eax and ln ax
5. Methods of differentiation
6. Differentiation of common functions
7. Differentiation of a product
8. Differentiation of a quotient
9. Function of a function
10. Successive differentiation
11. Some applications of differentiation
12. Rates of change
13. Velocity and acceleration
14. Turning points
15. Practical problems involving maximum
    and minimum values
16. Points of inflexion
17. Tangents and normals
18. Small changes
19. Differentiation of parametric equations
20. Some common parametric equations
21. Differentiation in parameters
22. Differentiation of implicit functions
23. Implicit functions
24. Differentiating implicit functions
25. Differentiating implicit functions containing products and quotients
26. Logarithmic differentiation
27. Differentiation of logarithmic functions
28. Differentiation of further logarithmic
    functions
29. Differentiation of [ f (x)]
30. Differentiation of hyperbolic functions
31. Standard differential coefficients of
    hyperbolic functions
32. Differentiation of inverse trigonometric
    and hyperbolic functions
33. Inverse functions
34. Differentiation of inverse trigonometric
    functions
35. Logarithmic forms of inverse hyperbolic
    functions
36. Differentiation of inverse hyperbolic
    functions
37. Partial differentiation
38. Introduction to partial derivatives
39. First-order partial derivatives
40. Second order partial derivatives
41. Total differential, rates of change and small
    changes
42. Total differential
43. Rates of change
44. Small changes
45. Maxima, minima and saddle points for
    functions of two variables