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

Answer 1

Emily Ammerman

#(dy)/dx = 6(2x-1)^2#

a simple technique to consider is using the chain rule which states

#(dy)/dx = dy/(du)*(du)/dx#

here # y=(2x-1)^3 and u=2x-1 #

# (du)/dx = 2#

# (dy)/(du) = 3(u)^2#

now we can also just not replace the #u# so

# (dy)/(du) = 3(2x-1)^2#

now we can solve #(dy)/dx = 6(2x-1)^2#

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Answer 2

Isaiah Allen

To find the derivative of ( (2x - 1)^3 ), use the chain rule.

Differentiate the outer function, which is ( u^3 ), with respect to ( u ), where ( u = 2x - 1 ). The derivative of ( u^3 ) is ( 3u^2 ).

Then, multiply by the derivative of the inner function ( u ) with respect to ( x ), which is 2.

[ \frac{d}{dx} (2x - 1)^3 = 3(2x - 1)^2 \times 2 ] [ = 6(2x - 1)^2 ]

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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.