Derivative Product Rule

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: \( (uv)' = u'v + uv' \).

Front

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

Back

The derivative is 18x^2 - 16x.

Front

If y = (x - 1)(x + 2), what is dy/dx?

Back

The derivative is 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 \( (cf)' = c f' \).

Front

Find f'(0) if f(x) = (x - 1)(x + 2).

Back

f'(0) = 1.

Front

What is the derivative of y = (x^2 - 1)(x + 7)?

Back

The derivative is 3x^2 + 14x - 1.

Front

How do you apply the Product Rule to find the derivative of y = u(x)v(x)?

Back

Differentiate u(x) to get u', then multiply by v(x). Next, differentiate v(x) to get v', then multiply by u(x). Finally, add the two results: \( u'v + uv' \).

Front

What is the derivative of a polynomial function?

Back

For a polynomial \( ax^n \), the derivative is \( n * ax^{n-1} \).

Front

If y = x^3 - 5x + 2, what is dy/dx?

Back

The derivative is 3x^2 - 5.

Front

What is the significance of the derivative in calculus?

Back

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