1. Quick Chain Rule Differentiation Type 1 Example
Differentiate y = √(3x3 + 2)

2. First put it into indices
y = √(3x3 + 2) = (3x3 + 2)½

3. y = √(3x3 + 2) = (3x3 + 2)½ Now Differentiate
dy/dx = ½(3x3 + 2)-½  9x2
Differentiate the inside of the bracket
Differentiate the bracket, leaving the inside unchanged

4. A General Rule for Differentiating y = (f(x))n
dy/dx = n(f(x))n-1  f ´(x)
Differentiate the bracket, leaving the inside unchanged
Differentiate the inside of the bracket

5. Quick Chain Rule Differentiation
Type 2 Example
Differentiate
y = e(x3+2)

6. y = e(x3+2) e(x3+2) Differentiating dy/dx = 3x2 
Write down the exponential function again
Multiply by the derrivative of the power

7. A General Rule for Differentiating
dy/dx = f ´(x) 
y = ef(x)
ef(x)
Multiply by the derrivative of the power
Write down the exponential function again

8. Quick Chain Rule Differentiation Type 3 Example
Differentiate y = In(x3 +2)

9. y = In(x3 +2) Now Differentiate dy/dx = 1  3x2 = 3x2 x3 + 2 x3 + 2
One over the bracket
Times the derrivative of the bracket

10. A General Rule for Differentiating
y = In(f(x))
dy/dx =  f ´(x) = f ´(x)
f(x) f(x)
Times the derrivative of the bracket
One over the bracket

11. f(x) e(f(x)) Summary f ´(x) e(f(x)) f ´(x) In(f(x))
n(f(x))n-1  f ´(x)
(f(x))n
dy/dx y