Q 18. - Calculus

Question

Find the derivatives of the functions: $f\left(x\right)={\log }_2(3x^2-5)$

Step-by-Step Solution

Answer

The required answer is $\frac{6x}{\ln 2(3x^2-5)}$.

Step 1. Given information.

The given function is: $f\left(x\right)={\log }_2(3x^2-5)$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right)={\log }_2(3x^2-5) \\ f\left(x\right)=\frac{d}{dx}{\log }_2(3x^2-5) \\ =\frac{1}{\ln 2(3x^2-5)}\frac{d}{dx}(3x^2-5) \\ =\frac{1}{\ln 2(3x^2-5)}\left[\frac{d}{dx}\left(3x^2\right)-\frac{d}{dx}\left(5\right)\right] \\ =\frac{1}{\ln 2(3x^2-5)}(6x-0) \\ =\frac{6x}{\ln 2(3x^2-5)} \end{gathered}$$