Solve 12^{4}-2^3+2^2-2^1+2^0a

$$12 ^ { 4 } - 2 ^ { 3 } + 2 ^ { 2 } - 2 ^ { 1 } + 2 ^ { 0 } a$$

Evaluate

$$a+20730$$

Solution Steps

Calculate 12 to the power of 4 and get 20736.

$$20736-2^{3}+2^{2}-2^{1}+2^{0}a$$

Calculate 2 to the power of 3 and get 8.

$$20736-8+2^{2}-2^{1}+2^{0}a$$

Subtract 8 from 20736 to get 20728.

$$20728+2^{2}-2^{1}+2^{0}a$$

Calculate 2 to the power of 2 and get 4.

$$20728+4-2^{1}+2^{0}a$$

Add 20728 and 4 to get 20732.

$$20732-2^{1}+2^{0}a$$

Calculate 2 to the power of 1 and get 2.

$$20732-2+2^{0}a$$

Subtract 2 from 20732 to get 20730.

$$20730+2^{0}a$$

Calculate 2 to the power of 0 and get 1.

$$20730+1a$$

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

$$20730+a$$

Differentiate w.r.t. a

$$1$$

Steps Using Derivative Rule for Sum

Calculate 12 to the power of 4 and get 20736.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20736-2^{3}+2^{2}-2^{1}+2^{0}a)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20736-8+2^{2}-2^{1}+2^{0}a)$$

Subtract 8 from 20736 to get 20728.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20728+2^{2}-2^{1}+2^{0}a)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20728+4-2^{1}+2^{0}a)$$

Add 20728 and 4 to get 20732.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20732-2^{1}+2^{0}a)$$

Calculate 2 to the power of 1 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20732-2+2^{0}a)$$

Subtract 2 from 20732 to get 20730.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20730+2^{0}a)$$

Calculate 2 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(20730+1a)$$

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}.

$$a^{1-1}$$

Subtract 1 from 1.

$$a^{0}$$

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

$$1$$