Question

Differentiate using product rule:

Answer 1

Here is the question:

\[h(x)=(x^2+5x+7).(x^3+2x-4)\]

Answer 2

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

Answer 3

let \[u = x^2 + 5x + 7 ===> \frac{du}{dx} = 2x + 5\]

\[v = x^3 + 3x - 4 ===> \frac{dv}{dx} = 3x^2 + 3\]

then \[\frac{dy}{dx} = u \times \frac{dv}{dx} + v \times \frac{ du}{dx}\]

Answer 4

just substitute and simplify

Answer 5

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

Answer 6

yes let me do it.

\[(x^2+5x+7) (3x^2+2) + (2x+5)(x^3+2x-4)\]

Answer 7

is that right?

Answer 8

yup. looks right to me

Answer 9

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

Answer 10

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

Answer 11

yes I have to simplify it after applying product rule.

Answer 12

a simple method is to draw up a grid