Derivatives - Product Rule

Front

What is the Product Rule in calculus?

Back

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

Front

Find the derivative of y = 2x^2 (3x - 4).

Back

18x^2 - 16x

Front

Let y = (x - 1)(x + 2). Find dy/dx.

Back

2x + 1

Front

What is the derivative of a constant multiplied by a function?

Back

If c is a constant and f(x) is a function, then the derivative is given by: (cf(x))' = c f'(x).

Front

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

Back

1

Front

What is the derivative of a product of two functions?

Back

The derivative of a product of two functions is found using the Product Rule: (uv)' = u'v + uv'.

Front

Find the derivative of y = x^2 (x + 1).

Back

3x^2 + x.

Front

What is the significance of the Product Rule?

Back

The Product Rule is essential for finding the derivative of products of functions, which is common in calculus.

Front

If u(x) = x^2 and v(x) = sin(x), what is the derivative of their product?

Back

(u'v + uv') = (2x sin(x) + x^2 cos(x)).

Front

What is the derivative of y = 5x^3 (2x^2 - 3)?

Back

30x^4 - 15x^3.