# Higher order derivatives

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