Derivatives and Integrals Flashcard

Front

What is the integral of x^(-2)?

Back

-1/x + C

Front

What is the integral of tan x sec x dx?

Back

sec x + C

Front

What is the integral of 1/x^3 dx?

Back

-1/2x^2 + C

Front

What is the integral of t^6 dt?

Back

1/7 t^7 + C

Front

What is the integral of cot x csc x dx?

Back

-csc x + C

Front

Define the derivative of a function.

Back

The derivative of a function measures the rate at which the function's value changes at a given point.

Front

What is the Fundamental Theorem of Calculus?

Back

It links the concept of differentiation and integration, stating that the integral of a function can be found using its antiderivative.

Front

What is the power rule for integration?

Back

For any real number n ≠ -1, ∫x^n dx = (1/(n+1))x^(n+1) + C.

Front

What is the chain rule in differentiation?

Back

The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function.

Front

What is the product rule in differentiation?

Back

The product rule states that the derivative of two functions multiplied together is given by: (u*v)' = u'v + uv'.