# doubts in derivatives

If s is distance and v is velocity, then: $$v=\frac{ds}{dt}$$and$$a=\frac{dv}{dt}$$ $$\frac{a}{v}=\frac{\frac{dv}{dt}}{\frac{ds}{dt}}$$ $$\frac{a}{v}=\frac{\frac{d}{dt}(\frac{ds}{dt})}{\frac{ds}{dt}}=\frac{dv}{ds}$$

I don't understand the last step .Is it possible? Numerator is first derivative whereas denominator is second derivative. Please explain it . Thanks.