Calc Review 2 for the Final Exam Derivative Basics & Rules UPDAT

Front

What is the derivative of a constant function, such as y = 2π?

Back

The derivative of a constant function is always 0.

Front

If y = \frac{x^2 - 9}{3x^2 + 8}, what is the formula for finding the derivative using the quotient rule?

Back

The derivative is given by \frac{(f'(x)g(x) - f(x)g'(x))}{(g(x))^2}, where f(x) = x^2 - 9 and g(x) = 3x^2 + 8.

Front

What is the derivative of the function y = 6e^{2x-5}?

Back

The derivative is y' = 12e^{2x-5}.

Front

How do you differentiate the function y = 4ln(x) + 8e^x - 9cos(x)?

Back

The derivative is y' = \frac{4}{x} + 8e^x + 9sin(x).

Front

What is the chain rule in differentiation?

Back

The chain rule states that if a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).

Front

What is the product rule for differentiation?

Back

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

Front

What is the quotient rule for differentiation?

Back

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

Front

What is the derivative of e^x?

Back

The derivative of e^x is e^x.

Front

What is the derivative of ln(x)?

Back

The derivative of ln(x) is \frac{1}{x}.

Front

What is the derivative of sin(x)?

Back

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