Question on: SS3 Mathematics - Differential Calculus (Differentiation)
Find the derivative of the function \(y = (2x + 1)(x^{2} + 2)\)
View related lesson
A
\(3x^{2} + x + 2\)
B
\(\2\left\lbrack 3x^{2} + x + 2 \right\rbrack\)
C
\(\x^{2} + x + 2\)
D
\(\frac{1}{2}\lbrack x^{2} + x + 3\rbrack\)
Ask EduPadi AI for a detailed answer
Correct Option: B
\[y = (2x + 1)(x^{2} + 2)\]
\[\frac{dy}{dx} = \frac{d(uv)}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}\]
\[u = (2x + 1),\ \ \ \ \ \ \ v = (x^{2} + 2)\]
\[\frac{du}{dx} = 2,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{dv}{dx} = 2x\]
\[\frac{dy}{dx} = (2x + 1)2x + \left( x^{2} + 2 \right)2\]
\[\frac{dy}{dx} = 4x^{2} + 2x + 2x^{2} + 4\]
\(\frac{dy}{dx} = 6x^{2} + 2x + 4 = 2\lbrack 3x^{2} + x + 2\rbrack\)
Add your answer
Please share this, thanks!
No responses