How do I solve derivative of $(2x^2+x+3)(5x+7)$ using product rule.

Question

I've to find the derivative of $$(2x^2+x+3)(5x+7)$$

Using product rule I get $$(2x^2+x+3)×5+5×(2x^2+x+3)\\20x^2+10x+30$$

Which is wrong. Please help, where I went wrong.

Answer 1

$y=(2x^2+x+3)(5x+7) $ then $$y'=(2x^2+x+3)'(5x+7)+(2x^2+x+3)(5x+7)'\\ =(4x+1)(5x+7)+5(2x^2+x+3) $$

Answer 2

You used product rule wrong, i.e., $$\dfrac{\mathrm d}{\mathrm dx}(f(x)g(x))=f(x)\dfrac{\mathrm d}{\mathrm dx}g(x)+g(x)\dfrac{\mathrm d}{\mathrm dx}f(x)$$

Therefore,$$(2x^2+x+3)\dfrac{\mathrm d}{\mathrm dx}(5x+7)+(5x+7)\dfrac{\mathrm d}{\mathrm dx}(2x^2+x+3)\\=(2x^2+x+3)×5+(5x+7)(4x+1)$$ $$=30x^2+38x+22$$