Solve -2^{4}-1^{4}-2-2^{3}-1^{2}+5-2^2-1^4++6-2-1^5-3-a^5-1

$$- 2 ^ { 4 } - 1 ^ { 4 } - 2 - 2 ^ { 3 } - 1 ^ { 2 } + 5 - 2 ^ { 2 } - 1 ^ { 4 } + + 6 - 2 - 1 ^ { 5 } - 3 - a ^ { 5 } - 1$$

Evaluate

$$-a^{5}-29$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$-16-1^{4}-2-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Calculate 1 to the power of 4 and get 1.

$$-16-1-2-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Subtract 1 from -16 to get -17.

$$-17-2-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Subtract 2 from -17 to get -19.

$$-19-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Calculate 2 to the power of 3 and get 8.

$$-19-8-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Subtract 8 from -19 to get -27.

$$-27-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Calculate 1 to the power of 2 and get 1.

$$-27-1+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Subtract 1 from -27 to get -28.

$$-28+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Add -28 and 5 to get -23.

$$-23-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Calculate 2 to the power of 2 and get 4.

$$-23-4-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Subtract 4 from -23 to get -27.

$$-27-1^{4}+6-2-1^{5}-3-a^{5}-1$$

Calculate 1 to the power of 4 and get 1.

$$-27-1+6-2-1^{5}-3-a^{5}-1$$

Subtract 1 from -27 to get -28.

$$-28+6-2-1^{5}-3-a^{5}-1$$

Add -28 and 6 to get -22.

$$-22-2-1^{5}-3-a^{5}-1$$

Subtract 2 from -22 to get -24.

$$-24-1^{5}-3-a^{5}-1$$

Calculate 1 to the power of 5 and get 1.

$$-24-1-3-a^{5}-1$$

Subtract 1 from -24 to get -25.

$$-25-3-a^{5}-1$$

Subtract 3 from -25 to get -28.

$$-28-a^{5}-1$$

Subtract 1 from -28 to get -29.

$$-29-a^{5}$$

Differentiate w.r.t. a

$$-5a^{4}$$

Steps Using Derivative Rule for Sum

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-16-1^{4}-2-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Calculate 1 to the power of 4 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-16-1-2-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Subtract 1 from -16 to get -17.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-17-2-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Subtract 2 from -17 to get -19.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-19-2^{3}-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-19-8-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Subtract 8 from -19 to get -27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-27-1^{2}+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-27-1+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Subtract 1 from -27 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-28+5-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Add -28 and 5 to get -23.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-23-2^{2}-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-23-4-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Subtract 4 from -23 to get -27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-27-1^{4}+6-2-1^{5}-3-a^{5}-1)$$

Calculate 1 to the power of 4 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-27-1+6-2-1^{5}-3-a^{5}-1)$$

Subtract 1 from -27 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-28+6-2-1^{5}-3-a^{5}-1)$$

Add -28 and 6 to get -22.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-22-2-1^{5}-3-a^{5}-1)$$

Subtract 2 from -22 to get -24.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-24-1^{5}-3-a^{5}-1)$$

Calculate 1 to the power of 5 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-24-1-3-a^{5}-1)$$

Subtract 1 from -24 to get -25.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-25-3-a^{5}-1)$$

Subtract 3 from -25 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-28-a^{5}-1)$$

Subtract 1 from -28 to get -29.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-29-a^{5})$$

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}.

$$5\left(-1\right)a^{5-1}$$

Multiply 5 times -1.

$$-5a^{5-1}$$

Subtract 1 from 5.

$$-5a^{4}$$