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

Text of Differentiate the following

Differentiate the following y=x^6 y= 3/x^3 y=x^3+3x^2-1/(2x^4 )

Chain RuleHow would you differentiate y = (x3+3)2Chain ruleDifferentiatey = (4x3 7x)6DifferentiateFind 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?There is a quicker way to differentiate functions of functions than using the chain rule

What is it?y = (x+2)2 differentiates to 2(x+2)

y = (x2 +1)2 differentiates to 4x(x2+1)

y = (x2 + 2x)3 differentiates to 3(2x+2)(x2+2x)2

Can you see the rule?RuleDifferentiate y = (3x4 + 5)5