Solve 5+z-(5^3)^2

$$5 + z - ( 5 ^ { 3 } ) ^ { 2 }$$

Evaluate

$$z-15620$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$5+z-5^{6}$$

Calculate 5 to the power of 6 and get 15625.

$$5+z-15625$$

Subtract 15625 from 5 to get -15620.

$$-15620+z$$

Differentiate w.r.t. z

$$1$$

Steps Using Derivative Rule for Sum

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}z}(5+z-5^{6})$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{\mathrm{d}}{\mathrm{d}z}(5+z-15625)$$

Subtract 15625 from 5 to get -15620.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-15620+z)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$z^{1-1}$$

Subtract 1 from 1.

$$z^{0}$$

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

$$1$$