Question

D d t [ 1 1 + t 2 ]?

Answer 1

`d/dt[11+2t]= 2` (If you meant `2t`)
`d/dt[11+t^2]= 2t` (If you meant `t^2`)

Explanation:

If you meant `2t`:
The derivative of a constant is always zero, since it's value doesn't change. The derivative of `2t` with respect to `t` is simply `2`. You can view the coefficient as the slope, which is essentially the definition of derivatives.

`d/dt[11+2t]= 2`

If you meant `t^2`:
The derivative of a constant will still be zero. For exponents, we can use the Power Rule:

Power Rule:
When differentiating, the exponent becomes the coefficient, and the power is decremented. In our case, the coefficient would be `2`, and the exponent would be `2-1` which is `1`.

`d/dt[11+t^2]= 2t`