Solve 1/4z/36

$$\frac { 1 } { 4 } \frac { z } { 36 }$$

Evaluate

$$\frac{z}{144}$$

Solution Steps

Multiply \frac{1}{4} times \frac{z}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{z}{4\times 36}$$

Multiply 4 and 36 to get 144.

$$\frac{z}{144}$$

Differentiate w.r.t. z

$$\frac{1}{144} = 0.006944444444444444$$

Steps Using Definition of a Derivative

Multiply \frac{1}{4} times \frac{z}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z}{4\times 36})$$

Multiply 4 and 36 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z}{144})$$

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

$$\frac{1}{144}z^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{144}z^{0}$$

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

$$\frac{1}{144}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{144}$$