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| Differentiation by Substitution |
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| Differentiation of certain functions seem to be very difficult, but by suitably substituting the independent variable with some trigonometric function or other functions, they can be differentiated easily. |
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| If f(x) involves inverse trigonometric functions of algebraic functions, the following substitutions simplify the function f(x) to be differentiated. |
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| Example 1: |
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| Differentiate |
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| Suggested answer: |
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| Example 2: |
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| Dividing the numerator and the denominator by cosq , we have |
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| Differentiating with respect to x, we have |
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