Differentiation
What is Differentiation?
● Part of calculus
● Process of finding the gradient of a curve at any point on the curve
● Finds derivative (the gradient function)
dy
dx
Basic Rules of Differentiation
● The derivative of xn is nxn−1
● The derivative of k xn is k nxn−1
● The derivative of a constant is 0
● The derivative of a sum (or difference) is the sum (or difference) of the
derivatives
● The points where the gradient of a curve is zero are called the stationary
points
Finding Tangents and Normals
● Use differentiation to find the gradient function
● Plug in the desired x-value to find the gradient of the curve at that point
● The gradient of a tangent will be the same
● The gradient of a normal will be the negative reciprocal
Increasing and Decreasing Functions
● If the gradient of a graph is positive, the value of y is increasing
● When the gradient of a graph is negative, the value of y is decreasing
What is Differentiation?
● Part of calculus
● Process of finding the gradient of a curve at any point on the curve
● Finds derivative (the gradient function)
dy
dx
Basic Rules of Differentiation
● The derivative of xn is nxn−1
● The derivative of k xn is k nxn−1
● The derivative of a constant is 0
● The derivative of a sum (or difference) is the sum (or difference) of the
derivatives
● The points where the gradient of a curve is zero are called the stationary
points
Finding Tangents and Normals
● Use differentiation to find the gradient function
● Plug in the desired x-value to find the gradient of the curve at that point
● The gradient of a tangent will be the same
● The gradient of a normal will be the negative reciprocal
Increasing and Decreasing Functions
● If the gradient of a graph is positive, the value of y is increasing
● When the gradient of a graph is negative, the value of y is decreasing
