2.2 Derivatives Flashcard #1 (GCF's out)

Front

What is the derivative of the function f(x) = 3x^4 - 5x^2 + 7?

Back

f'(x) = 2x(6x^2 - 5)

Front

What is the general formula for the derivative of x^n?

Back

f'(x) = nx^(n-1)

Front

Find the derivative of the function f(x) = x^3 + x^2 + 3.

Back

f'(x) = x(3x + 2)

Front

What is the derivative of the function f(x) = 1 - x^2?

Back

f'(x) = -2x

Front

Find the derivative of the function f(x) = x^2 + 1/x and simplify with GCF out.

Back

f'(x) = (2x^3 - 1)/x^2

Front

What does GCF stand for in the context of derivatives?

Back

GCF stands for Greatest Common Factor, which is used to simplify expressions.

Front

How do you find the derivative of a polynomial function?

Back

Use the power rule: f'(x) = n*x^(n-1) for each term.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = nx^(n-1).

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

How do you apply the product rule in differentiation?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.