Calculus Solutions Ex#3.1

Q.01 (a) Find $\frac{d y}{d x}$ by differentiating implicitly. Solution: $$ y=x+x y-2 x^{3}=2—(1) $$ Differentiating w.r.t $x$ $$ \begin{aligned} & \frac{d}{d x}\left[x+x y-2 x^{3}\right]=\frac{d}{d x}[2] \\ \\ & \frac{d}{d x}[x]+\frac{d}{d x}[x y]-2 \frac{d}{d x}\left[x^{3}\right]=0 \\ \\ & 1+x \frac{d y}{d x}+y \frac{d}{d x}[x]-2\left(3 x^{3-1}\right)=0 \\ \\ & 1+\frac{x d y}{d x}+y-6 x^{2}=0 \\ \\ … Read more