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**Quick Chain Rule Differentiation Type 1 Example **

Differentiate y = √(3x3 + 2)

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**First put it into indices**

y = √(3x3 + 2) = (3x3 + 2)½

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**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

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**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

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**Quick Chain Rule Differentiation**

Type 2 Example Differentiate y = e(x3+2)

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**y = e(x3+2) e(x3+2) Differentiating dy/dx = 3x2 **

Write down the exponential function again Multiply by the derrivative of the power

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**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

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**Quick Chain Rule Differentiation Type 3 Example **

Differentiate y = In(x3 +2)

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**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

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**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

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**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

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