Differentiation

Front

What is differentiation?

Back

Differentiation is a mathematical process used to find the rate at which a function is changing at any given point, represented by the derivative.

Front

What is the derivative of y = 3x^2 - 4x + 2?

Back

6x - 4

Front

What is the derivative of y = 5x^4?

Back

20x^3

Front

How do you find the equation of the tangent line to a curve at a given point?

Back

To find the equation of the tangent line, calculate the derivative at the point to find the slope, then use the point-slope form of the line.

Front

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

Back

3x^2 + 2x

Front

Given f(x) = 3x^2 + 2x, find the gradient of the tangent where x = -3.

Back

-16

Front

What is the power rule in differentiation?

Back

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

Front

What is the product rule in differentiation?

Back

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

Front

What is the quotient rule in differentiation?

Back

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

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing where its derivative is positive and decreasing where its derivative is negative.