Power rule and product rule problem

AI Thread Summary
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.
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(2x+3)^3(x-4)
How do I differentiate this?
 
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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:
Ok. Thanks!
 
\frac{dy}{dx}=3(2x+3)^2(2) + 1
Right?
 
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)
 
I got it! Thank you!
 

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