Differentiation

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Quotient Rule

Suppose we want to differentiate $y=\frac{2x-5}{5x-2}$`y`=2`x`−55`x`−2 using the quotient rule.

a

Using the substitution $u=2x-5$`u`=2`x`−5, find $u'$`u`′.

b

Using the substitution $v=5x-2$`v`=5`x`−2, find $v'$`v`′.

c

Hence find $y'$`y`′.

d

Is it possible for the derivative of this function to be zero?

No

A

Yes

B

No

A

Yes

B

Easy

Approx 5 minutes

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