Derivatives - All Rules Precalc

Front

What is the quotient rule for derivatives?

Back

If f = u/v, then f' = (vu' - uv')/v².

Front

How do you find the derivative of a constant function, such as f(x) = 7?

Back

The derivative of a constant function is 0.

Front

What is a derivative in calculus?

Back

A derivative represents the rate of change of a function with respect to a variable.

Front

Given y = (x+2)/(x-3), how do you find y'?

Back

Use the quotient rule: y' = -5/(x-3)².

Front

What is the power rule for derivatives?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the product rule for derivatives?

Back

If f = u*v, then f' = u'v + uv'.

Front

How do you differentiate a sum of functions?

Back

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

Front

What is the chain rule for derivatives?

Back

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

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).