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Quick Chain Rule Differentiation Type 1 Example Differentiate y = √ (3x 3 + 2). First put it into indices y = √ (3x 3 + 2) = (3x 3 + 2) ½. y = √ (3x 3 + 2) = (3x 3 + 2) ½ Now Differentiate dy/dx = ½(3x 3 + 2) -½ 9x 2. Differentiate the inside of the bracket.

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

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**Quick Chain Rule Differentiation**Type 1 Example Differentiate y = √(3x3 + 2)**First put it into indices**y = √(3x3 + 2) = (3x3 + 2)½**y = √(3x3 + 2) = (3x3 + 2)½**Now Differentiate dy/dx = ½(3x3 + 2)-½9x2 Differentiate the inside of the bracket Differentiate the bracket, leaving the inside unchanged**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**Quick Chain Rule Differentiation**Type 2 Example Differentiate y =e(x3+2)**y =e(x3+2)**Differentiating dy/dx = 3x2 e(x3+2) Write down the exponential function again Multiply by the derrivative of the power**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**Quick Chain Rule Differentiation**Type 3 Example Differentiate y = In(x3 +2)**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**A General Rule for Differentiating**y = In(f(x)) dy/dx = 1 f´(x) = f´(x) f(x)f(x) Times the derrivative of the bracket One over the bracket**y**dy/dx (f(x))n n(f(x))n-1 f´(x) e(f(x)) f´(x)e(f(x)) In(f(x)) f´(x) f(x) Summary

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