Solve p-(p-(p-(p-p)))

$$p - ( p - ( p - ( p - p ) ) )$$

Evaluate

$$p$$

Solution Steps

Combine p and -p to get 0.

$$p-\left(p-\left(p-0\right)\right)$$

Multiply -1 and 0 to get 0.

$$p-\left(p-\left(p+0\right)\right)$$

Anything plus zero gives itself.

$$p-\left(p-p\right)$$

Combine p and -p to get 0.

$$p-0$$

Multiply -1 and 0 to get 0.

$$p+0$$

Anything plus zero gives itself.

$$p$$

Differentiate w.r.t. p

$$1$$

Steps Using Definition of a Derivative

Combine p and -p to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-\left(p-\left(p-0\right)\right))$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-\left(p-\left(p+0\right)\right))$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-\left(p-p\right))$$

Combine p and -p to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p-0)$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p+0)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p)$$

The derivative of ax^{n} is nax^{n-1}.

$$p^{1-1}$$

Subtract 1 from 1.

$$p^{0}$$

For any term t except 0, t^{0}=1.

$$1$$