Solve (6b-6-b^4)+(b^4-3-4b)

$$( 6 b - 6 - b ^ { 4 } ) + ( b ^ { 4 } - 3 - 4 b )$$

Evaluate

$$2b-9$$

Solution Steps

Combine -b^{4} and b^{4} to get 0.

$$6b-6-3-4b$$

Subtract 3 from -6 to get -9.

$$6b-9-4b$$

Combine 6b and -4b to get 2b.

$$2b-9$$

Differentiate w.r.t. b

$$2$$

Steps Using Derivative Rule for Sum

Combine -b^{4} and b^{4} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6b-6-3-4b)$$

Subtract 3 from -6 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}b}(6b-9-4b)$$

Combine 6b and -4b to get 2b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b-9)$$

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}.

$$2b^{1-1}$$

Subtract 1 from 1.

$$2b^{0}$$

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

$$2\times 1$$

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

$$2$$