Derivatives - Product Rule and Trig Derivatives

Front

What is the Product Rule for derivatives?

Back

If u(x) and v(x) are functions, then the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

Find the derivative of f(x) = (x - 1)(x + 2) using the Product Rule.

Back

f'(x) = (1)(x + 2) + (x - 1)(1) = 2x + 1.

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

What is the derivative of tan(x)?

Back

The derivative of tan(x) is sec²(x).

Front

What is the derivative of cot(x)?

Back

The derivative of cot(x) is -csc²(x).

Front

What is the derivative of sec(x)?

Back

The derivative of sec(x) is sec(x)tan(x).

Front

What is the derivative of csc(x)?

Back

The derivative of csc(x) is -csc(x)cot(x).

Front

If f(x) = (x - 1)(x + 2), what is f'(0)?

Back

f'(0) = 1.

Front

What is the chain rule in differentiation?

Back

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