Solve any maths problem

Step by step

1. \frac{d}{dt}\left[\frac{x}{t - 1}\right]

   Start from the derivative to compute.

2. x \frac{d}{d t} \frac{1}{t - 1}

   Constant multiple rule: pull the constant out.

3. - \frac{x \frac{d}{d t} \left(t - 1\right)}{\left(t - 1\right)^{2}}

   Reciprocal rule: (1/v)′ = −v′/v² with v = t - 1.

4. - \frac{x \left(\frac{d}{d t} \left(-1\right) + \frac{d}{d t} t\right)}{\left(t - 1\right)^{2}}

   Sum rule: differentiate term by term.

5. - \frac{x \frac{d}{d t} t}{\left(t - 1\right)^{2}}

   The derivative of a constant is 0.

6. - \frac{x}{\left(t - 1\right)^{2}}

   d/dx of x is 1.