Question

Derivative of $f\left(x\right)=\frac{x^2}{\cos x}$ is

• A. $\frac{2x\cos x+x^2\sin x}{\sin x}$
• B. $\frac{2x\cos x+x^2\sin x}{\cos x}$
• C. $\frac{2x\cos x+x^2\sin x}{{\cos }^{2}x}$
• D. $\frac{2x\cos x-x^2\sin x}{{\cos }^{2}x}$

Answer 1

The correct option is C $\frac{2x\cos x+x^2\sin x}{{\cos }^{2}x}$

Given, $f\left(x\right)=\frac{x^2}{\cos x}$
So, derivative of the function is given as
$\frac{df\left(x\right)}{dx}=\frac{d\left(\frac{x^2}{\cos x}\right)}{dx}$
Using Division method we have
$\Rightarrow \frac{\cos x\frac{d{x}^2}{dx}-x^2\frac{d\cos x}{dx}}{(\cos x{)}^2}$
$\Rightarrow \frac{2x\cos x+x^2\sin x}{{\cos }^{2}x}$