Product/Quotient/Chain Rule Review

Front

What is the Product Rule in differentiation?

Back

The Product Rule states that if you have two functions u(x) and v(x), the derivative of their product is given by: (u*v)' = u'v + uv'.

Front

What is the Quotient Rule in differentiation?

Back

The Quotient Rule states that if you have two functions u(x) and v(x), the derivative of their quotient is given by: (u/v)' = (u'v - uv')/v^2.

Front

What is the Chain Rule in differentiation?

Back

The Chain Rule states that if you have a composite function f(g(x)), the derivative is given by: (f(g(x)))' = f'(g(x)) * g'(x).

Front

Differentiate f(x) = 5sin(x) + 3x^3cos(x). What is f'(x)?

Back

f'(x) = 5cos(x) - 3x^3sin(x) + 9x^2cos(x).

Front

Find the derivative of y = 2x^2(3x - 4). What is y'?

Back

y' = 18x^2 - 16x.

Front

Differentiate (2x + 2)(x - 5)^8 with respect to x. What is the derivative?

Back

The derivative is 8(2x + 2)(x - 5)^7 + 2(x - 5)^8.

Front

Back

Front

Find the derivative of f(t) = (t^2 + 2t)^5. What is f'(t)?

Back

f'(t) = 5(t^2 + 2t)^4(2t + 2).

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

If f(x) = x^n, what is f'(x)?

Back

f'(x) = nx^{n-1}.