Flashcards
Differentiation from first principles
Cards in this deck (5)
- 1Diagram of y=x^3 using x
- 2The gradient of the tangent at x=1 is also the same as....The gradient of the chord
- 3The gradient of the tangent to f(x) at the point (x=a) is :lim(h->0)(f(a+h)-f(a))/h
- 4When we have the gradient of a tangent e.g. lim(h->0)(10x+7+h) , what is the derivative?f'(x) = 10x+7 , as we limit h to 0, therefore when h=0, it does nothing so is ignored.
- 5Find the derivative of f(x)=x^2+3x-4 from first principlesF(x+h) = (x+h)^2+3(x+h)-4 ; use equation (f(x+h) - f(x) /h) , ((x+h)^2+3(x+h)-4) - (x^2+3x-4) /h cancels to 2x+3+h. There when we limit x to 0, the derivative is f'(x)=2x+3