Find and classify the stationary points on the curve y= x 2 e x .
Find and classify the stationary points on the curve y= x2ex.
We need a rule to simplify these cases.
Find the derivative of x3 +1 :
Find the derivative of (x3 +1)2 :
x6+2x3+1we need to expand first:
3x2
6x5+6x
6x2(x3+1)
But, what if we have to find the derivative of (x3 +1)8?
We need a rule to simplify these cases.
The chain rule
By the end of the lesson you will be able to:
• Find the derivative of composite functions by applying the chain rule.
The following functions are a composition of other two simpler functions. Can you identify them?
andas in:
The expression y = ( x3+1)2 is a composition of two simpler functions :
y= u2 and u= x3+1
f(x) = x2 and g(x)= x3+1
f(g(x))= (x3+1)2
or
The chain rule says :
y = f(u) ⇒
In the example: y = (x3+1)2
y =u2 and u = x3+1
Find if y = (3x1)7 :
Find if y = 5(1x)3 :
Find if
Find if
Find if y =(x2+1)100
Find the derivative of y = sin (4x)
Find if
Find where the tangent to cuts the xaxis.
at x =0
Consider the function for
What is the domain of f ?
Find and hence find intervals where f(x)
is increasing.
A body moves along the xaxis with displacement
function
where t is the time in seconds,
Find the velocity and acceleration functions for the motion of the body.
Solve Book: page 212 Ex 7A : at least 5 exercises of each question.
http://www.mathsbingo.com/DifferentiationChainRule.html
At the end of the lesson: