Solve P(a+h)-P(a)/a+h-a

$$\frac { P ( a + h ) - P ( a ) } { a + h - a }$$

Evaluate

$$P$$

Short Solution Steps

Combine a and -a to get 0.

$$\frac{P\left(a+h\right)-Pa}{h}$$

Factor the expressions that are not already factored.

$$\frac{Ph}{h}$$

Cancel out h in both numerator and denominator.

$$P$$

Differentiate w.r.t. P

$$1$$

Steps Using Definition of a Derivative

Combine a and -a to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{P\left(a+h\right)-Pa}{h})$$

Factor the expressions that are not already factored in \frac{P\left(a+h\right)-Pa}{h}.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{Ph}{h})$$

Cancel out h in both numerator and denominator.

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

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.

$$1$$