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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
Now Differentiate dy/dx = ½(3x 3 + 2) -½ 9x 2 Differentiate the bracket, leaving the inside unchanged Differentiate the inside of the bracket
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 (x 3 +2)
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)
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)
Quick Chain Rule Differentiation Type 3 Example Differentiate y = In(x 3 +2)
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
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
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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Page 20 The Chain Rule is called the Power Rule, and recall that I said cant be done by the power rule because the base is an expression more complicated.
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