Quick Chain Rule Differentiation

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Quick Chain Rule Differentiation Type 1
Example Differentiate y v(3x3 2)
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First put it into indices y v(3x3 2) (3x3
2)½
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y v(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(x32)
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y e(x32)
Differentiating dy/dx 3x2 ?
e(x32)
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 1 ? f (x) f (x)
f(x) f(x)
Times the derrivative of the bracket
One over the bracket
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Summary