If #f(x)= cot5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule?
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( f(g(x)) ) using the chain rule, follow these steps:
-
Compute the derivative of the outer function ( f(x) ) with respect to its inner function ( g(x) ). This is denoted as ( f'(g(x)) ).
-
Compute the derivative of the inner function ( g(x) ) with respect to ( x ), denoted as ( g'(x) ).
-
Multiply ( f'(g(x)) ) by ( g'(x) ).
-
Substitute ( g(x) ) back into the resulting expression.
Applying this to ( f(g(x)) = \cot^5(g(x)) ) and ( g(x) = 2x^2 - 1 ):
-
Compute ( f'(g(x)) ) by finding the derivative of ( \cot^5(x) ), which is ( -5\cot^4(x)\csc^2(x) ).
-
Compute ( g'(x) ) by finding the derivative of ( 2x^2 - 1 ), which is ( 4x ).
-
Multiply ( f'(g(x)) ) by ( g'(x) ) to get ( -20x\cot^4(2x^2 - 1)\csc^2(2x^2 - 1) ).
Therefore, the derivative of ( f(g(x)) ) with respect to ( x ) using the chain rule is ( -20x\cot^4(2x^2 - 1)\csc^2(2x^2 - 1) ).
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(t)=sin^2(e^(sin^2t))# using the chain rule?
- How do you implicitly differentiate #1=-xy+x+y-y^2+x^2#?
- How do you find the derivative of #f(x) = 2/(x-1) - 1/(x+2) #?
- What is the implicit derivative of #25=sin(xy)/(3xy)#?
- How do you use implicit differentiation to find #(dy)/(dx)# given #3x^2y^2=4x^2-4xy#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7