If the slope of the tangent drawn to the curve $y=e^{a+b x^2}$ at the point $P(1,1)$ is -2 , then the value of $2 a-3 b$ is

If $f(x)=\sum_{p=1}^7 p^2 \sin ^{-1}\left(\frac{4}{5} \sin (p x)-\frac{3}{5} \cos (p x)\right)$, then the value of $\frac{d f}{d x}$ at $x=1$ is [given that $\sin ^{-1}(\sin x)=x$ ])

If $y=\frac{a x+b}{c x+d}$, then $\frac{d x}{d y}=$

If $x^2+y^2=t-\frac{1}{t}, x^4+y^4=t^2+\frac{1}{t^2}$, then $\frac{d y}{d x}=$