(Y2:9) Differentiation

Why must you use radians

Trig calculus relies on small angle approximations

Sin ≈ x

Cos x ≈ 1-1/2 x²

Tan x ≈ x

What is the chain rule and when is it valid to use

Dy/dx=dy/du ×du/dx

Is used when you have a function in a function (e.g. (x+2)²)

Where u is set to be the inner function

If you have dy/dx how to get dx/dy

Find the reciprocal 1 ÷ dy/dx

What is Product rule and when is it valid to use

dy/dx = udv/dx + vdu/dx. Where u and v are your functions

Uses when you have the product of 2(or more) functions y=uv

What is the quotation rule and when is it valid to use

dy/dx = (vdu/dx - udv/dx)/v² where u and v are your functions

Uses when you have a function divided by another

Y=u/v

When is function concave and convex

Concave: if f’’(x)≤0 for every value on range

Convex: if f’’(x)≥0 for every value on range

What is a point of inflation

When f’’(x) changes sign

What are these implicitly differentiated

f(y)

y^n

xy

f(y)→ f'(y)dy/dx

y^n → ny^(n+1) dy/ex

xy → X dy/dx +y