Question

use the product rule of differentiation to determine the dy/dx of (2x-1)^2 (3x + 5)^4

Answer 1

For f(x)*g(x) the product rule is: f'(x)*g(x) + f(x)*g'(x) where f'(x) is the derivative of f(x) and the same for g'(x).

Here, f(x) is (2x-1)^2 and g(x) is (3x+5)^4.

So \[f'(x) = 2(2x-1) \times 2\]
\[g'(x)=4(3x+5)^3 \times 3\]
so it'll look like this:


\[\frac{ d }{ dx }(2x-1)^2 (3x + 5)^4 =2 \times 2(2x-1) (3x + 5)^4 + 4 \times 3 (2x-1)^2 (3x + 5)^3\]

Answer 2

thanks for ur solution