Solve 3^2z^2/5^23^2

$$\frac { 3 ^ { 2 } z ^ { 2 } } { 5 ^ { 2 } 3 ^ { 2 } }$$

Evaluate

$$\frac{z^{2}}{25}$$

Solution Steps

Cancel out 3^{2} in both numerator and denominator.

$$\frac{z^{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{z^{2}}{25}$$

Differentiate w.r.t. z

$$\frac{2z}{25}$$

Steps Using Definition of a Derivative

Cancel out 3^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{2}}{5^{2}})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{2}}{25})$$

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

$$2\times \frac{1}{25}z^{2-1}$$

Multiply 2 times \frac{1}{25}.

$$\frac{2}{25}z^{2-1}$$

Subtract 1 from 2.

$$\frac{2}{25}z^{1}$$

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

$$\frac{2}{25}z$$