3B Survey Review

Front

What is the derivative of the function y = e^(5x)?

Back

The derivative y' = 5e^(5x).

Front

What is the Chain Rule in calculus?

Back

The Chain Rule is a formula for computing the derivative of the composition of two or more functions.

Front

How do you find the derivative of a function at a specific point?

Back

To find the derivative at a point, you can use the limit definition of the derivative or apply differentiation rules.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

What is the product rule in calculus?

Back

The product rule states that if you have two functions u(x) and v(x), then the derivative of their product is u'v + uv'.

Front

What is the quotient rule in calculus?

Back

The quotient rule states that if you have two functions u(x) and v(x), then the derivative of their quotient is (u'v - uv')/v^2.

Front

What does it mean for a function to be differentiable at a point?

Back

A function is differentiable at a point if it has a derivative at that point, meaning it is smooth and has no sharp corners.

Front

What is the significance of the derivative in real-world applications?

Back

The derivative represents the rate of change of a quantity, which can be used to model motion, growth, and other dynamic systems.

Front

How do you apply the Chain Rule to find the derivative of composite functions?

Back

To apply the Chain Rule, differentiate the outer function and multiply it by the derivative of the inner function.

Front

What is the derivative of y = x^n?

Back

The derivative y' = nx^(n-1).