# How do you differentiate #x * (4-x^2)^(1/2)#?

I found:

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

To differentiate ( x \cdot (4-x^2)^{\frac{1}{2}} ), use the product rule and the chain rule.

- Apply the product rule: ((uv)' = u'v + uv').
- Let ( u = x ) and ( v = (4-x^2)^{\frac{1}{2}} ).
- Find ( u' ) and ( v' ) using the chain rule.
- ( u' = 1 )
- ( v' = \frac{1}{2}(4-x^2)^{-\frac{1}{2}} \cdot (-2x) )

- Plug the values into the product rule formula: [ \frac{d}{dx}(x \cdot (4-x^2)^{\frac{1}{2}}) = 1 \cdot (4-x^2)^{\frac{1}{2}} + x \cdot \frac{1}{2}(4-x^2)^{-\frac{1}{2}} \cdot (-2x) ]
- Simplify the expression.

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 the derivative of #Y= x^2 ( x + 1 )^3#?
- How do you use the chain rule to differentiate #f(x)=sin(1/(x^2+1))#?
- Suppose that #f'(x) = 2x# for all #x#. What is #f(2)# if #f(1)=0#? What if #f(-2) = 3#?
- If #f(x) =sec^3(x/2) # and #g(x) = sqrt(2x-1 #, what is #f'(g(x)) #?
- How do you find the derivative of # ln[x]/x^(1/3)#?

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