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What is the derivative of #f(x) = x^2(x-2)^4#?

Answer 1

William Abdalla

William Abdalla

#(df)/(dx)=2x(x-2)^3(3x-2)#

Product rule states that if #f(x)=g(x)*h(x)#

#(df)/(dx) = g(x)xx(dh)/(dx) + h(x)xx(dg)/(dx) #

Here #g(x)=x^2# and #h(x)=(x-2)^4#

Hence, #(df)/(dx)=x^2xx4(x-2)^3+(x-2)^4xx2x#

= #2x(x-2)^3{2x+(x-2)}#

= #2x(x-2)^3(3x-2)#

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Answer 2

Ezra Adams

To find the derivative of ( f(x) = x^2(x-2)^4 ), you can use the product rule and the chain rule. The derivative is given by:

[ f'(x) = 2x(x-2)^4 + x^2 \cdot 4(x-2)^3 ]

Simplifying:

[ f'(x) = 2x(x-2)^4 + 4x^2(x-2)^3 ]

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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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