Higher order derivatives

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  1. The concept of higher order derivatives
  1. 1st1^{st} and 2nd2^{nd} derivatives.
    Find the first and second derivative for the following functions:
    1. f(x)=x4+5x2+3x+2 f(x)=x^4+5x^2+3x+2
    2. f(t)=sin(2t) f(t)=\sin (2t)
    3. g(s)=(2s+5s2)7g(s)=(2s+5s^2)^7
    4. y=5 y=5
    5. f(x)=5lnx f(x)=5 \ln x
  2. 2nd2^{nd} derivatives with implicit differentation
    Find y"y" by implicit differentiation for the following functions:
    1. x2+y2=9 x^2+y^2=9
    2. x2+xy=9 x^2+xy=9
  3. Derivatives with repeating patterns
    Find f(100)(x)f^{(100)}(x) for the following functions:
    1. f(x)=sin(x) f(x)= \sin (x)
    2. f(x)=e(2x) f(x)=e^{(2x)}
Topic Notes
If f(x)f'(x) is the derivative of f(x)f(x), then we say that f"(x)f"(x) is the 2nd2^{nd} derivative of f(x)f(x). Similarly, f(n)(x)f^{(n)}(x) is the nthn'th derivative of f(x)f(x).