AP Calculus AB Derivatives

Front

Derive y=(Sin3x)²

Back

6Cos(3x)Sin(3x)

Front

What is the derivative of sin(x)?

Back

cos(x)

Front

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t. What is the acceleration of the object at time t = 2 s?

Back

66 m/s/s

Front

Find the derivative of y = 2x²(3x - 4)

Back

18x² - 16x

Front

The velocity of an object is given as v = 2t + 3t³. What is the acceleration of the object at t = 2 s?

Back

38 m/s/s

Front

What is the power rule for differentiation?

Back

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

Front

What is the product rule for differentiation?

Back

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

Front

What is the chain rule for differentiation?

Back

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

Front

What is the derivative of e^x?

Back

e^x

Front

What is the derivative of ln(x)?

Back

1/x