2.2 Derivatives Flashcard #2

Front

What is the derivative of f(x) = 5/x^2?

Back

Front

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

Back

f'(x) = 4x(x^2 + 3x - 1)

Front

If f(x) = ax^2 + 2bx, what are a and b if f'(x) = 8x + 6?

Back

a = 4 and b = 3

Front

Back

Front

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

Back

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

Front

What is the power rule for differentiation?

Back

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

Front

What is the product rule for differentiation?

Back

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

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

Differentiate f(x) = 3x^5 - 4x^3 + 2x - 1.

Back

f'(x) = 15x^4 - 12x^2 + 2.