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Differentiation by the Chain Rule 2omework Find the derivatives of the following: 1. Y (3x ! 8)4(y 9 12(3 x ! 8)y 9 30 x (3 × 2 + 2) 315. Y 2!5(3)(4 ! 9 x) y9 2 135(4 ! 9 x) y9 2 2 2 × 7. Y $ #2
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How to fill out tifferentiation by form chain
How to fill out tifferentiation by form chain
01
Step 1: Identify the function that needs to be differentiated using the chain rule.
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Step 2: Break down the function into separate functions where each function represents a specific sub-expression.
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Step 3: Differentiate each sub-expression separately using basic differentiation rules.
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Step 4: Write down the derivative of each sub-expression.
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Step 5: Multiply the derivatives of each sub-expression together, connecting them with multiplication symbols.
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Step 6: Simplify the resulting expression by combining like terms if possible.
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Step 7: The final simplified expression represents the derivative of the original function using the chain rule.
Who needs tifferentiation by form chain?
01
Differentiation by the chain rule is needed in calculus when dealing with composite functions.
02
Composite functions are functions that involve the composition (combination) of two or more functions, where the output of one function becomes the input of another.
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Examples of situations where differentiation by the chain rule is required include finding the derivative of functions involving trigonometric functions, exponential functions, logarithmic functions, and compositions of functions.
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This technique allows for the calculation of derivatives of complex functions by breaking them down into simpler, more manageable parts.
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