Visions of Mathematics: Differential Calculus

Differential Calculus

1. Even function $f(-x) = f(x)$

2. Odd function   $f(-x) = -f(x)$

3. Perodic function   $f(x+nT) = f(x)$

4. Inverse function

5. Linear Function   $y = ax+b \: \: where \: \: a = tan \: \alpha$

6. Quadratic Function   $y = ax^2 + bx +c$

7. Cubic Function $y = x^3$

8. $y = ax^3 + bx +cx$

9. Power function

10. Exponential Function

11. Hyperbolic Sine Function

$y = sinh\: x\, , sinh\: x = \frac{e^x-e^{-x}}{2}$

12. Hyperbolic Cosine Function

$y = cosh\: x\, , cosh\: x = \frac{e^x+e^{-x}}{2}$

13. Hyperbolic Tangent Function

$y = tanh\: x\, , tanh\: x = \frac{sinhx}{coshx} = \frac{e^x-e^{-x}}{e^x+e^{-x}}$

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