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

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Presentation on theme: "Quick Chain Rule Differentiation Type 1 Example Differentiate y = √ (3x 3 + 2)"— Presentation transcript:

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

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

3 Now Differentiate dy/dx = ½(3x 3 + 2) -½  9x 2 Differentiate the bracket, leaving the inside unchanged Differentiate the inside of the bracket

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 (x 3 +2)

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

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

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

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

10 A General Rule for Differentiating y = In(f(x)) dy/dx = 1  f ´(x) = f ´(x) f(x) One over the bracket Times the derrivative of the bracket

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


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