Semester 1 Final Review

Front

What is the derivative of tan(x)?

Back

sec²(x)

Front

What is the Pythagorean theorem?

Back

a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

Front

What is the derivative of the function f(x) = e^x?

Back

e^x

Front

If a function has a derivative that is negative, what does that tell you?

Back

The function is decreasing.

Front

What does the derivative of a function represent?

Back

The rate of change of the function with respect to its variable.

Front

What is the chain rule in differentiation?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the product rule in differentiation?

Back

If u and v are functions of x, then d(uv)/dx = u'v + uv'.

Front

What is the quotient rule in differentiation?

Back

If u and v are functions of x, then d(u/v)/dx = (u'v - uv')/v².

Front

What is the definition of a limit?

Back

The value that a function approaches as the input approaches some value.

Front

What is the difference between a function's increasing and decreasing intervals?

Back

Increasing intervals are where the function's output rises as the input rises; decreasing intervals are where the output falls as the input rises.