# How do you differentiate #y = -2 /root3x#?

It is

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

To differentiate ( y = -\frac{2}{\sqrt{3x}} ), you would use the chain rule of differentiation. The derivative is:

[ \frac{dy}{dx} = \frac{d}{dx}\left(-\frac{2}{\sqrt{3x}}\right) = \frac{2}{2\sqrt{3x}} \cdot \frac{d}{dx}(\sqrt{3x}) = \frac{1}{\sqrt{3x}} \cdot \frac{d}{dx}(3x) = \frac{1}{\sqrt{3x}} \cdot 3 = \frac{3}{\sqrt{3x}} = \frac{3}{\sqrt{3}\sqrt{x}} = \frac{3}{\sqrt{3}x^{\frac{1}{2}}} = \frac{3}{\sqrt{3}x^{\frac{1}{2}}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{3x} = \frac{\sqrt{3}}{x} ]

So, the derivative of ( y = -\frac{2}{\sqrt{3x}} ) with respect to ( x ) is ( \frac{\sqrt{3}}{x} ).

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.

- How do you find #(d^2y)/(dx^2)# for #5x^2=5y^2+4#?
- How do you differentiate #f(x)= e^x/(e^(x-2) -4 )# using the quotient rule?
- How do you use implicit differentiation to find #(dy)/(dx)# given #1=3x+2x^2y^2#?
- How do you differentiate #-1=xy^3-x^2y#?
- How do you differentiate #f(x)=cscx# using the quotient rule?

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