# If #f(x)= csc7 x # and #g(x) = e^(1 +3x ) #, 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, you follow these steps:

- Compute the derivative of the outer function with respect to its inner function.
- Multiply by the derivative of the inner function with respect to ( x ).

Applying this to ( f(g(x)) ), where ( f(x) = \csc(7x) ) and ( g(x) = e^{1 + 3x} ), the derivative is:

[ \frac{d}{dx}\left( \csc(7e^{1 + 3x}) \right) = -7\csc(7e^{1 + 3x})\cot(7e^{1 + 3x})\cdot 3e^{1 + 3x} ]

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 differentiate #sqrtt*(1-t^2)#?
- How do you differentiate #f(x)=(x+2)^2(x-5)^3# using the product rule?
- How do you find the derivative of #1/x^5#?
- How do you differentiate #(3x-4/x)^2 (1-x+7x^2)^4#?
- What is the slope of the tangent line of # (3x)/y-(4x^2)/(1-y)^2 =C #, where C is an arbitrary constant, at #(1,2)#?

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