First slide

Derivatives

Question

$If f (x) = |\begin{array}{ccc} x & x^{2} & x^{3} \\ 1 & 2 x & 3 x^{2} \\ 0 & 2 & 6 x \end{array}| then f^{'} (x) =$

Moderate

A

0
B

$x^{2}$
C

$3 x^{2}$
D

$6 x^{2}$

Solution

$f (x) = |\begin{matrix} x & x^{2} & x^{3} \\ 1 & 2 x & 3 x^{2} \\ 0 & 2 & 6 x \end{matrix}| \cdot f' (x) = |\begin{matrix} 1 & 2 x & 3 x^{2} \\ 1 & 2 x & 3 x^{2} \\ 0 & 2 & 6 x \end{matrix}| + |\begin{matrix} x & x^{2} & x^{3} \\ 0 & 2 & 6 x \\ 0 & 2 & 6 x \end{matrix}| + |\begin{matrix} x & x^{2} & x^{3} \\ 1 & 2 x & 3 x^{2} \\ 0 & 0 & 6 \end{matrix}| = 0 + 0 + 6 (2 x^{2} - x^{2}) = 6 x^{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App