Question

If $y=xtanx$, then $dy/dx$ is equal to

• A. $\frac{tanx}{x-x^2-y^2}$
• B. $\frac{y}{x-x^2-y^2}$
• C. $\frac{tanx}{y-x}$
• D. $\frac{cosxsinx+x}{co{s}^{2}x}$

Answer 1

Answer: (D)

We have, $y=xtanx$
$\therefore \frac{dy}{dx}=x{\left(tanx\right)}^{\prime }+tanx\cdot {\left(x\right)}^{\prime }$
$=xse{c}^{2}x+tanx\cdot 1$
$=\frac{x}{co{s}^{2}x}+\frac{sinx}{cosx}=\frac{x+sinxcosx}{co{s}^{2}x}$