Higher Order Derivatives in Calculus
Higher Order Derivatives in Calculus

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Higher-Order Derivatives

We know how to take some derivatives, but what if we want to find the second derivative, or more? To do that, we simply differentiate again! First, however, let’s go over the notation:

First Derivative: f ‘ (x)

Second Derivative: f ” (x)

Third Derivative: f ”’ (x)

Fourth Derivative: f (4) (x)

nth derivative: f (n) (x)

Now, for some examples; we’ll start off with a relatively easy one. Find the third derivative of the function:

Here is another. Find the second derivative of the function:

Here is one which involves the product rule. Find the second derivative:

And one more, this time with the quotient rule. Note that we can simplify this one before differentiating, but lets use it as is for practice:

Now, for the second derivative:

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