Implicit & Inverse Differentiation Glossary

Rule for differentiating composites: d/dx[f(g(x))] = f_prime(g(x))*g_prime(x).

f(g(x)) - one function applied to result of another.

y written directly as f(x).

Derivatives of derivatives: second, third, etc.

Differentiating when y is not solved explicitly, treating y as f(x).

Equation relating x and y not solved for y.

In f(g(x)), g(x) is evaluated first.

g_prime(y) = 1/f_prime(g(y)) when f_prime(g(y)) is nonzero.

arcsin, arccos, arctan, arcsec, arccsc, arccot.

Take ln of both sides before differentiating. For variable exponents.

In f(g(x)), f is applied to g(x).