Question

Differentiate $\frac{3x}{1+2x^4}$ w.r.t $x$

Answer 1

let, $y=\frac{3x}{1+2x^4}$

differentiating on both sides w.r.t x

$\frac{dy}{dx}=\frac{3(1+2x^4)-\left(3x\right)\left(x^3\right)}{(1+2x^4)}$

$(\because \frac{\left(f\right(x\left)g\right(x\left)\right)}{dx}=\frac{f^{\prime }\left(x\right)g\left(x\right)-g^{\prime }\left(x\right)f\left(x\right)}{{\left(g\right(x\left)\right)}^2})$

$=\frac{3-6x^4-24x^4}{(1+2x^4{)}^2}$

$\frac{dy}{dx}=\frac{3-18x^4}{(1+2x^4{)}^2}$