Quick warm up - Basic Derivatives

Front

What is the derivative of a function?

Back

The derivative of a function measures how the function's output value changes as its input value changes. It represents the slope of the tangent line to the function's graph at a given point.

Front

What is the power rule for differentiation?

Back

The power rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1), where n is a constant.

Front

Find the derivative of f(x) = x^4 + 4x^3 - 2x^2.

Back

f'(x) = 4x^3 + 12x^2 - 4x.

Front

How do you differentiate a constant?

Back

The derivative of a constant is zero.

Front

What is the derivative of a constant function?

Back

If f(x) = c (where c is a constant), then f'(x) = 0.

Front

What is the derivative of f(x) = 5x^3 - 2x?

Back

f'(x) = 15x^2 - 2.

Front

What is the derivative of a linear function?

Back

The derivative of a linear function f(x) = mx + b is simply the slope m.

Front

Find the derivative of g(x) = 6 + (2/3)x.

Back

g'(x) = 2/3.

Front

How do you find the derivative at a specific point, such as f'(2) for f(x) = x^2 + 2x?

Back

To find f'(2), first find the derivative f'(x), then substitute x = 2 into the derivative.

Front

What is the derivative of f(x) = x^2?

Back

f'(x) = 2x.