Inverse Trigonometric Differentiation Rules
This discussion will focus on the basic Inverse Trigonometric Differentiation Rules. There are two different inverse function notations for trigonometric functions. The inverse function for sinx can be written as sin-1x or arcsin x.
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DERIVATIVE |
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DERIVATIVE |
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Let's look at some examples:
Step 1: Apply the Constant Multiple Rule.
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Constant Mul. |
Step 2: Take the derivative of cos-1x. |
Arccos Rule
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Step 1: Apply the chain rule.
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g = sin-1 x u = sin-1 x f = u3 |
Step 2: Take the derivative of both functions. |
Derivative of f = u3 Original 3u2 Power
__________________________ Derivative of g = sin-1 x Original Arcsin Rule
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Step 3: Substitute the derivatives and the original expression for the variable u into the Chain Rule and simplify.
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Chain Rule Sub for u
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Step 1: Apply the quotient rule.
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Step 2: Take the derivative of each part. Apply the appropriate trigonometric differentiation rule. |
Original Constant Multiple Rule Arctan Rule
__________________________ Original Sum Rule 0 + 2x Constant/Power
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Step 3: Substitute the derivatives & simplify. |
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Related Links: Math algebra Logarithmic Differentiation Implicit Differentiation Algebra Topics |
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