Basic AP Calculus AB Derivative and Integration Formulas

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero. It represents the slope of the tangent line to the graph of the function at that point.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = n*x^(n-1), where n is a constant.

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then the derivative of their product is given by (uv)' = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u(x) and v(x) are functions, then the derivative of their quotient is given by (u/v)' = (u'v - uv')/v^2.

Front

What is the chain rule for differentiation?

Back

If a function y = f(g(x)), then the derivative is given by dy/dx = f'(g(x)) * g'(x).

Front

What is the definition of an integral?

Back

An integral represents the accumulation of quantities, such as area under a curve. The definite integral of a function from a to b is the limit of a Riemann sum as the number of partitions approaches infinity.

Front

What is the Fundamental Theorem of Calculus?

Back

The Fundamental Theorem of Calculus states that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x)dx = F(b) - F(a).

Front

What is the formula for the integral of x^n?

Back

∫ x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1 and C is the constant of integration.

Front

What is the formula for the integral of e^x?

Back

∫ e^x dx = e^x + C, where C is the constant of integration.

Front

What is the formula for the integral of sin(x)?

Back

∫ sin(x) dx = -cos(x) + C, where C is the constant of integration.