Higher order derivatives:
Let y = f(x)
First derivative ![1237_Higher order derivatives.png](https://www.expertsmind.com/../CMSImages/1237_Higher order derivatives.png)
Second derivative ![1683_Higher order derivatives1.png](https://www.expertsmind.com/../CMSImages/1683_Higher order derivatives1.png)
Third derivative
etc.
Example: Find out the 2nd derivative of ax3 + bx2 + cx + d.
Solution : Let y = ax3 + bx2 + cx + d.
![1950_Higher order derivatives3.png](https://www.expertsmind.com/../CMSImages/1950_Higher order derivatives3.png)
The Logarithmic Differentiation
If u and v are the functions of independent variable x then to differentiate functions like uv , first we take log and then differentiate.
Example: Differentiate
with respect to sin( m cos- 1x).
Solution: Let y = (log x)tan x and z = sin(m cos- 1x)
So logy = tanx log log x
![1483_Higher order derivatives5.png](https://www.expertsmind.com/CMSImages/1483_Higher%20order%20derivatives5.png)
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