Power rule and product rule problem

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Start date Jan 27, 2005
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Power Power rule Product Product rule

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To differentiate the function (2x+3)^3(x-4), the product rule is applied, defined as y'(x) = f'(x)g(x) + f(x)g'(x). The first function, f(x), is (2x+3)^3, and its derivative f'(x) is calculated using the power rule, resulting in f'(x) = 3(2x+3)^2(2). The second function, g(x), is (x-4), with its derivative g'(x) equal to 1. The final derivative is obtained by combining these results correctly. Careful application of these rules is essential for accurate differentiation.

Jan 27, 2005

footprints

(2x+3)^3(x-4)
How do I differentiate this?

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Jan 27, 2005

courtrigrad

Use the product rule: vdu + udv. For the first function use the power rule: x^n = nx^{n-1} \frac{du}{dx}=(3(2x+3)^2(2)

Last edited: Jan 27, 2005

Jan 27, 2005

footprints

Ok. Thanks!

Jan 27, 2005

footprints

\frac{dy}{dx}=3(2x+3)^2(2) + 1
Right?

Jan 27, 2005

arildno

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No!
You must be more careful!
Define:
f(x)=(2x+3)^{3},g(x)=(x-4)
Then,
y(x)=f(x)g(x),y'(x)=f'(x)g(x)+f(x)g'(x)
You need therefore to calculate f'(x) and g'(x)

Jan 27, 2005

footprints

I got it! Thank you!

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