Solve b-(-1)^8-3*(-1)^5+(-1)^16=

$$b - ( - 1 ) ^ { 8 } - 3 \cdot ( - 1 ) ^ { 5 } + ( - 1 ) ^ { 16 } =$$

Evaluate

$$b+3$$

Solution Steps

Calculate -1 to the power of 8 and get 1.

$$b-1-3\left(-1\right)^{5}+\left(-1\right)^{16}$$

Calculate -1 to the power of 5 and get -1.

$$b-1-3\left(-1\right)+\left(-1\right)^{16}$$

Multiply 3 and -1 to get -3.

$$b-1-\left(-3\right)+\left(-1\right)^{16}$$

The opposite of -3 is 3.

$$b-1+3+\left(-1\right)^{16}$$

Add -1 and 3 to get 2.

$$b+2+\left(-1\right)^{16}$$

Calculate -1 to the power of 16 and get 1.

$$b+2+1$$

Add 2 and 1 to get 3.

$$b+3$$

Differentiate w.r.t. b

$$1$$

Steps Using Derivative Rule for Sum

Calculate -1 to the power of 8 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b-1-3\left(-1\right)^{5}+\left(-1\right)^{16})$$

Calculate -1 to the power of 5 and get -1.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b-1-3\left(-1\right)+\left(-1\right)^{16})$$

Multiply 3 and -1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b-1-\left(-3\right)+\left(-1\right)^{16})$$

The opposite of -3 is 3.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b-1+3+\left(-1\right)^{16})$$

Add -1 and 3 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b+2+\left(-1\right)^{16})$$

Calculate -1 to the power of 16 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b+2+1)$$

Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b+3)$$

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}.

$$b^{1-1}$$

Subtract 1 from 1.

$$b^{0}$$

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

$$1$$