Differentiation - created from Mind Map

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Differentiation quiz

Why? To find the gradient of a curve at a point

How to differentiate?

The gradient of a function has different names

Differentiate dy/dx to get the second order differential

How to find maximum and minimum values of the function

Equivalent to finding the gradient of the tangent to the curve at that point

Gradient of equation is change in y divided by change in x

y-y1=m(x-x1)

m=(y-y1) /(x-x1)

Gradient of a tangent= dy/dx

y=x3

at x =1, y=1

dy/dx = 3x^2

so at x=1, gradient = 3.

Gradient of normal is the negative inverse of m or negative inverse dy/dx

y=x3

at x =1, y=1

dy/dx = 3x^2

so at x=1, gradient = 3.

Normal = - 1/m

So at x=1, y=1 gradient = -1/3

A gradient is the rate of change

Differentiating a polynomial function (one variable)

Differenting polynomials

Chain Rule

Chain Rule Slides

Product Rule

Product Rule

Quotient Rule

Quotient Rule

Natural Logarithm and Exponential functions

Natural Log Function

Natural exponential function

Trig Functions

Trig functions

The gradient function

The derived function with respect to x

The differential coefficient with respect to x

The first differential with respect to x

dy/dx

f'(x)

The second order differential has different names

d^2y/dx^2

f''(x)

The second derivative of a function

At maximum and minimum values of f(x), f'(x) = 0.

At maximum value, f''(x) is negative

At minimum value, f''(x) is positive