How do you find the derivative of #(1-y^2)^(1/2)#?
Using substitution, the derivative is:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the derivative of ( (1 - y^2)^{1/2} ), you can use the chain rule. The chain rule states that if you have a function ( f(g(x)) ), the derivative with respect to ( x ) is ( f'(g(x)) \times g'(x) ).
Let ( u = 1 - y^2 ). Then, ( \frac{du}{dy} = -2y ).
Now, let ( f(u) = u^{1/2} ). The derivative of ( f(u) ) with respect to ( u ) is ( \frac{df}{du} = \frac{1}{2}u^{-1/2} ).
By applying the chain rule, we get:
[ \frac{d}{dy}(1 - y^2)^{1/2} = \frac{df}{du} \times \frac{du}{dy} ] [ = \frac{1}{2}(1 - y^2)^{-1/2} \times (-2y) ] [ = -\frac{y}{(1 - y^2)^{1/2}} ]
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 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 differentiate #f(x)=1/(x^7-2)# using the quotient rule?
- How do you compute the derivative for #f(x)=sin^2(7x+5)+cos^2(7x+5)#?
- How do you differentiate #x^7 - 8xy + y^4 = 7#?
- How do you differentiate #y = (x + 7)^10 (x^2 + 2)^7#?
- How do you differentiate #f(x) = 5/(x^3+4)# 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