Derivatives

Front

What is a derivative?

Back

A derivative represents the rate at which a function is changing at any given point, essentially the slope of the tangent line to the curve of the function.

Front

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

Back

3x^2 + 2x

Front

Find the derivative of f(x) = -4x.

Back

-4

Front

What do we find when we take the derivative of a function?

Back

The slope of the tangent line.

Front

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

Back

18x^2 - 16x

Front

What is the derivative of e^x?

Back

e^x

Front

What is the power rule for derivatives?

Back

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

Front

Find the derivative of f(x) = 5x^4.

Back

20x^3

Front

What is the product rule for derivatives?

Back

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

Front

Find the derivative of f(x) = sin(x).

Back

cos(x)