3.3-3.5 Review

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

Front

How do you find the derivative of a sum of functions?

Back

The derivative of a sum of functions is the sum of their derivatives: (f + g)' = f' + g'.

Front

What is the derivative of f(x) = ax^n?

Back

The derivative is f'(x) = n*ax^(n-1).

Front

What is the product rule for differentiation?

Back

The product rule states that if u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

The quotient rule states that if u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

What is the derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

How do you find the slope of the tangent line to a function at a given point?

Back

The slope of the tangent line at a point is found by evaluating the derivative of the function at that point.

Front

What is the chain rule for differentiation?

Back

The chain rule states that if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).