midterm calculus honors 2024

Front

What is the derivative of y = (2x + 1)^{10}?

Back

y' = 20(2x + 1)^{9}

Front

Find the derivative of y = \frac{x^{2}}{3x - 1}.

Back

y' = \frac{3x^{2} - 2x}{(3x - 1)^{2}}

Front

What is the slope of y = 3x^{2} - 5 at x = 2?

Back

The slope is 12.

Front

Find the slope of f(x) = -3x^{2} - 6x at x = 1.

Back

m = -12.

Front

What is \frac{d}{dx} \arcsin(x)?

Back

\frac{d}{dx} \arcsin(x) = \frac{1}{\sqrt{1 - x^{2}}}

Front

What is the power rule for differentiation?

Back

If y = x^{n}, then y' = nx^{n-1}.

Front

What is the product rule for differentiation?

Back

If y = u(x)v(x), then y' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If y = \frac{u(x)}{v(x)}, then y' = \frac{u'v - uv'}{v^{2}}.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then y' = f'(g(x))g'(x).

Front

What is the derivative of y = e^{x}?

Back

y' = e^{x}.