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Chain Rule for Derivatives

The Chain Rule formula is as follows:

If f(x)=g (h(x)), then f'(x)=g' (h(x)) h'(x).

Let me show you an example how to use this formula:

Example; Find derivative of f(x)= sin (3x2+x).

Solution: In this question imagine f(x) is composed of two functions -- g(x)=sinx and h(x)=3x2+x, and h(x) is the inner function in the formula. So according to the formula f'(x)=g' (h(x)) h'(x), we get this:

f'(x)=cos(3x2+x) *(6x+1)=(6x+1) cos(3x2+x)

Note that the derivative of sin x is cos x, that's why we get cos(3x2+x), and (6x+1) is the derivative of 3x2+x

  • Subject : Math
  • Topic : Calculus
  • Posted By : Jason

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