The derivative of y = cos^(-1)(x) is dy/dx = -1/√(1-x^2).
If y = cos^(-1)(x), then what is dy/dx?
Practice Questions
Q1
If y = cos^(-1)(x), then what is dy/dx?
-1/√(1-x^2)
1/√(1-x^2)
1/x
-1/x
Questions & Step-by-Step Solutions
If y = cos^(-1)(x), then what is dy/dx?
Correct Answer: dy/dx = -1/√(1-x^2)
Step 1: Understand that y = cos^(-1)(x) means y is the angle whose cosine is x.
Step 2: Recall the relationship between the derivative of the inverse cosine function and its derivative formula.
Step 3: The formula for the derivative of y = cos^(-1)(x) is dy/dx = -1/√(1 - x^2).
Step 4: This formula is derived from the fact that the derivative of cos(y) with respect to y is -sin(y), and using implicit differentiation.
Inverse Trigonometric Functions – Understanding the derivatives of inverse trigonometric functions, specifically the derivative of the arccosine function.
Chain Rule – Applying the chain rule in differentiation when dealing with inverse functions.
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