# How do you use the chain rule to differentiate #y=(3x^2+1)^4#?

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

To differentiate ( y = (3x^2 + 1)^4 ) using the chain rule, follow these steps:

- Identify the outer function ( u ) and the inner function ( v ). In this case, ( u = v^4 ) and ( v = 3x^2 + 1 ).
- Differentiate the outer function with respect to the inner function. ( \frac{du}{dv} = 4v^3 ).
- Differentiate the inner function with respect to ( x ). ( \frac{dv}{dx} = 6x ).
- Apply the chain rule formula: ( \frac{dy}{dx} = \frac{du}{dv} \cdot \frac{dv}{dx} ).
- Substitute the derivatives found in steps 2 and 3 into the chain rule formula.
- Simplify the expression to get the final answer.

Therefore, the derivative of ( y = (3x^2 + 1)^4 ) with respect to ( x ) is ( \frac{dy}{dx} = 4(3x^2 + 1)^3 \cdot 6x ). Simplify this expression to get the final result.

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

- How do you find the Implicit differentiation of #x^4-5xy^3+y^6=21#?
- If #f(x)= csc7 x # and #g(x) = e^(1 +3x ) #, how do you differentiate #f(g(x)) # using the chain rule?
- How do you differentiate #f(x)=csc(sqrt(e^x)) # using the chain rule?
- How do you differentiate #y=sin(4x)#?
- How do you differentiate # y=sec^2 (3 - 8x)# using the chain rule?

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