Solve 2/3z3/4=

$$\frac { 2 } { 3 } z \frac { 3 } { 4 } =$$

Evaluate

$$\frac{z}{2}$$

Solution Steps

Multiply \frac{2}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3}{3\times 4}z$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{4}z$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}z$$

Differentiate w.r.t. z

$$\frac{1}{2} = 0.5$$

Steps Using Definition of a Derivative

Multiply \frac{2}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{2\times 3}{3\times 4}z)$$

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{2}{4}z)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{2}z)$$

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

$$\frac{1}{2}z^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}z^{0}$$

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

$$\frac{1}{2}\times 1$$

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

$$\frac{1}{2}$$