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Mathematics
OpenStudy (anonymous):

Differentiate using product rule:

OpenStudy (anonymous):

Here is the question: \[h(x)=(x^2+5x+7).(x^3+2x-4)\]

OpenStudy (anonymous):

right? \[(2x+5)(3x^2+2) \]

OpenStudy (campbell_st):

let \[u = x^2 + 5x + 7 ===> \frac{du}{dx} = 2x + 5\] \[v = x^3 + 3x - 4 ===> \frac{dv}{dx} = 3x^2 + 3\] then \[\frac{dy}{dx} = u \times \frac{dv}{dx} + v \times \frac{ du}{dx}\]

OpenStudy (campbell_st):

just substitute and simplify

OpenStudy (anonymous):

(f(x).g(x))' = f(x).g'(x) + g(x).f'(x)

OpenStudy (anonymous):

yes let me do it. \[(x^2+5x+7) (3x^2+2) + (2x+5)(x^3+2x-4)\]

OpenStudy (anonymous):

is that right?

OpenStudy (anonymous):

yup. looks right to me

OpenStudy (anonymous):

Now, I am confuse with the next part. I cannot simplify. :(

OpenStudy (campbell_st):

normally you would be expected to simplify.... not sure on your question requirements

OpenStudy (anonymous):

yes I have to simplify it after applying product rule.

OpenStudy (campbell_st):

a simple method is to draw up a grid |dw:1338113768920:dw|

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