Derivatives of a composite function:
Given a composite function y = f(x), that is a function denoted by y = F(u), u = Φ(x) or y = FΦ[(x)], then ![1032_Derivatives of a composite function.png](https://www.expertsmind.com/../CMSImages/1032_Derivatives of a composite function.png)
This is called as chain rule. The rule can be extended to any number of composite variables;
For example if y = f(u(v)), then ![2370_Derivatives of a composite function4.png](https://www.expertsmind.com/CMSImages/2370_Derivatives%20of%20a%20composite%20function4.png)
Example: Find out dy/dx
![1019_Derivatives of a composite function1.png](https://www.expertsmind.com/../CMSImages/1019_Derivatives of a composite function1.png)
Solution:
![2249_Derivatives of a composite function2.png](https://www.expertsmind.com/../CMSImages/2249_Derivatives of a composite function2.png)
![1226_Derivatives of a composite function3.png](https://www.expertsmind.com/../CMSImages/1226_Derivatives of a composite function3.png)
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