# Methods of Differentiation

There are many methods of differentiation that we can use for differentiating complicated functions. For these flash cards, all you have to do is state which rule(s) you would use to differentiate them! If you want to practise differentiating them, the answer (but not method) is on the back as well. Be warned though: some of these are quite complicated to differentiate!

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• Created by: M Toynbee
• Created on: 07-10-15 08:40
y = sin^7(x)
Chain rule: dy/dx = 7sin^6(x)cos(x)
1 of 7
y = e^(x)ln(x)
Product rule: dy/dx = e^(x)/x + ln(x)e^(x)
2 of 7
y = tan(x) / (x^2)
Quotient rule: dy/dx = ((x^2)sec^2(x) - 2xtan(x)) / (x^4)
3 of 7
y = ln(cos(x))
Chain rule: dy/dx = -tan(x)
4 of 7
y = xsin(11x)
Product and chain rules: dy/dx = 11xcos(11x) + sin(11x)
5 of 7
y = (x^2)(e^x) / sin(x)
Product and quotient rules: dy/dx = (sin(x)[(x^2)(e^x) + 2x(e^(x))] - cos(x)[(x^2)(e^x)]) / sin^2(x)
6 of 7
y = cos(x^3) / e^(x^3))
Quotient and chain rules: dy/dx = [-3(x^2)(e^(x^3))[sin(x^3) + cos(x^3)]] / ((e^(x^3))^2)
7 of 7

## Other cards in this set

### Card 2

y = e^(x)ln(x)

#### Back

Product rule: dy/dx = e^(x)/x + ln(x)e^(x)

### Card 3

#### Front

y = tan(x) / (x^2)

y = ln(cos(x))

y = xsin(11x)