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# Computing Derivatives

# Computing Derivatives Using Implicit Differentiation

We've taken lots of derivatives of explicit functions. In fact, so far we've only taken derivatives of explicit functions. We've had an equation for *y* (or *f*, or whatever) and we've used our collection of rules to find *f '*.

We can also take derivatives of implicit functions. If we have an equation relating *x* and *y*, we can take derivatives first and solve for *y'* later.

We can use either Leibniz or Lagrange notation.

It will be helpful to have a variation on Lagrange notation. The expression (...) means, "take the derivative, with respect to *x*, of whatever is in the parentheses." It essentially means the same thing as (...)', but with the added precise statement that yes, we are taking the derivative with respect to *x* and not with respect to anything else.

For example,

and

Remember, means the same thing as a prime.

(*f* + *g*)' = *f*' + *g*'

We can say