If y=tan ^{-1}left(frac{3 x-x^3}{1-3 x^2}righ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given, $y=	an ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}ight)+	an ^{-1}\left(\frac{4 x-4 x^3}{1-6 x^2+x^4}ight)$.Substitute $x=	an 	heta$, then $\

Vedclass · Accepted Answer

$\frac{7}{1+x^2}$

Vedclass · Answer

(D) Given, $y=	an ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}ight)+	an ^{-1}\left(\frac{4 x-4 x^3}{1-6 x^2+x^4}ight)$.Substitute $x=	an 	heta$, then $	heta = 	an^{-1} x$.The expression becomes:$y = 	an^{-1}(	an 3	heta) + 	an^{-1}(	an 4	heta)$.This simplifies to $y = 3	heta + 4	heta = 7	heta$.Substituting back, $y = 7 	an^{-1} x$.Differentiating with respect to $x$:$\frac{d y}{d x} = 7 	imes \frac{1}{1+x^2} = \frac{7}{1+x^2}$.

If $y=\tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\tan ^{-1}\left(\frac{4 x-4 x^3}{1-6 x^2+x^4}\right)$, then $\frac{d y}{d x}$ is equal to

Similar Questions

If $\tan ^{-1} x+\tan ^{-1} y=\frac{4 \pi}{5}$,then $\cot ^{-1} x+\cot ^{-1} y$ is equal to

If for $|x|>1$, $\tanh ^{-1}\left(\frac{1}{x}\right)+\operatorname{coth}^{-1}(x)=\log _e(f(x))$, then $f(-5)=$

The value of $\tan \left\{\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right\}$ is

If $\sin ^{-1} x < \cos ^{-1} x$, then

The value of $\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module