How do you find the derivative of #y = (3x + 1)^2#?

Answer 1

Use chain rule / Expand

Method 1 #y=(3x+1)^2# Assume the function in the bracket as some other variable say t. #t = 3x+1# #dt/dx = 3# #y = t^2# #dy/dx = dy/dt * dt/dx# #=2t*3# #dy/dx=6(3x+1)#

Method 2: If you are able to find the derivative by expanding everything

#y = (3x+1)^2# # y = 9x^2+6x+1# #dy/dx = 18x+6# #dy/dx = 6(3x+1)#
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Answer 2

To find the derivative of ( y = (3x + 1)^2 ), you can apply the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. The derivative of ( (3x + 1)^2 ) with respect to ( x ) is ( 2(3x + 1) \times (3) ), which simplifies to ( 6(3x + 1) ). Therefore, the derivative of ( y ) with respect to ( x ) is ( 6(3x + 1) ).

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Answer from HIX Tutor

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.

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