Solve 19^3-22^2-4a+16

$$19 ^ { 3 } - 22 ^ { 2 } - 4 a + 16$$

Evaluate

$$6391-4a$$

Solution Steps

Calculate 19 to the power of 3 and get 6859.

$$6859-22^{2}-4a+16$$

Calculate 22 to the power of 2 and get 484.

$$6859-484-4a+16$$

Subtract 484 from 6859 to get 6375.

$$6375-4a+16$$

Add 6375 and 16 to get 6391.

$$6391-4a$$

Differentiate w.r.t. a

$$-4$$

Steps Using Derivative Rule for Sum

Calculate 19 to the power of 3 and get 6859.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6859-22^{2}-4a+16)$$

Calculate 22 to the power of 2 and get 484.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6859-484-4a+16)$$

Subtract 484 from 6859 to get 6375.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6375-4a+16)$$

Add 6375 and 16 to get 6391.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6391-4a)$$

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}.

$$-4a^{1-1}$$

Subtract 1 from 1.

$$-4a^{0}$$

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

$$-4$$