# Given that # sin(x/y) = 1/2 # find #dy/dx#?

# dy/dx = y/x #

We have:

By signing up, you agree to our Terms of Service and Privacy Policy

To find ( \frac{dy}{dx} ) from the equation ( \sin\left(\frac{x}{y}\right) = \frac{1}{2} ), we use implicit differentiation:

Differentiating both sides with respect to ( x ), we get:

[ \frac{d}{dx} \left( \sin\left(\frac{x}{y}\right) \right) = \frac{d}{dx} \left( \frac{1}{2} \right) ]

Using the chain rule, we have:

[ \cos\left(\frac{x}{y}\right) \cdot \frac{1}{y} \cdot \frac{dy}{dx} = 0 ]

Solving for ( \frac{dy}{dx} ), we get:

[ \frac{dy}{dx} = 0 ]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- When you use the quotient rule to find the derivative of a function, does the denominator of the function have to have a variable or can it be a constant number?
- How do you implicitly differentiate #-1=xy^2+2x^2y-e^ysin(3x+y) #?
- What is the derivative of #xsqrt(1-x)#?
- If #f(x) = 4x -2# and #g(x) = e^(3x-1)#, what is #f'(g(x)) #?
- How do you differentiate #f(x)=(lnx+3x)(cotx-e^x)# using the product rule?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7