Math Problem Statement
Find dy/dx if -y = sin^(-3)(x).
Solution
The given equation is:
We need to find . To do this, we can differentiate both sides of the equation with respect to .
Starting with the given equation:
- Differentiate both sides with respect to :
- Applying the chain rule to the left side:
- Applying the chain rule to the right side:
Let , then . Differentiating with respect to gives:
Putting these together, we get:
- Multiplying both sides by -1 to solve for :
Thus, the derivative is:
Would you like more details on any specific step or have any further questions?
Here are some related questions that might interest you:
- How do we use the chain rule in differentiation?
- What is the difference between implicit and explicit differentiation?
- How can the derivative of a function with a trigonometric term be interpreted graphically?
- How would the derivative change if the function was (-y
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Trigonometric Functions
Formulas
Chain Rule: d(u^n)/dx = n * u^(n-1) * du/dx
Trigonometric Derivative: d(sin(x))/dx = cos(x)
Theorems
Chain Rule
Suitable Grade Level
Grades 11-12