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Differentiate the following. Chain Rule. How would you differentiate y = (x 3 +3) 2. Chain rule. If you have a function within a function then we need to use the chain rule If y = [f(x)] n then let u = f(x) and y = u n then, . Differentiate. y = (4x 3 – 7x) 6. Differentiate. - PowerPoint PPT Presentation
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Differentiate the following
Chain Rule
How would you differentiate y = (x3+3)2
Chain ruleO If you have a function within a
function then we need to use the chain rule
If y = [f(x)]n then let u = f(x) and y = un
then,
DifferentiateO y = (4x3 – 7x)6
Differentiate
𝑦=1
√𝑥2+5
Find the equation of the tangent of y = (4x + 2)4 at the point (2, 1000)
Easier way?
Do we have to use the chain rule?
O There is a quicker way to differentiate functions of functions than using the chain rule
O What is it?
O y = (x+2)2 differentiates to 2(x+2)
O y = (x2 +1)2 differentiates to 4x(x2+1)
O y = (x2 + 2x)3 differentiates to 3(2x+2)(x2+2x)2
O Can you see the rule?
RuleO If y = [f(x)]n then
Differentiate y = (3x4 + 5)5
Differentiate
Find the value of dy/dx at (2, 1/3) if
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