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

Learn how to apply the chain rule in differentiation by solving three different examples: square root, exponential, and natural logarithm functions.

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

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  1. Quick Chain Rule Differentiation Type 1 Example Differentiate y = √(3x3 + 2)

  2. First put it into indices y = √(3x3 + 2) = (3x3 + 2)½

  3. 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

  4. 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

  5. Quick Chain Rule Differentiation Type 2 Example Differentiate y =e(x3+2)

  6. y =e(x3+2) Differentiating dy/dx = 3x2 e(x3+2) Write down the exponential function again Multiply by the derrivative of the power

  7. 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

  8. Quick Chain Rule Differentiation Type 3 Example Differentiate y = In(x3 +2)

  9. 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

  10. 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

  11. 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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