Solve (9b^2+b-2)+(-5b^2-2b+8)

$$( 9 b ^ { 2 } + b - 2 ) + ( - 5 b ^ { 2 } - 2 b + 8 )$$

Evaluate

$$4b^{2}-b+6$$

Solution Steps

Combine 9b^{2} and -5b^{2} to get 4b^{2}.

$$4b^{2}+b-2-2b+8$$

Combine b and -2b to get -b.

$$4b^{2}-b-2+8$$

Add -2 and 8 to get 6.

$$4b^{2}-b+6$$

Differentiate w.r.t. b

$$8b-1$$

Steps Using Derivative Rule for Sum

Combine 9b^{2} and -5b^{2} to get 4b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b^{2}+b-2-2b+8)$$

Combine b and -2b to get -b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b^{2}-b-2+8)$$

Add -2 and 8 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b^{2}-b+6)$$

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}.

$$2\times 4b^{2-1}-b^{1-1}$$

Multiply 2 times 4.

$$8b^{2-1}-b^{1-1}$$

Subtract 1 from 2.

$$8b^{1}-b^{1-1}$$

Subtract 1 from 1.

$$8b^{1}-b^{0}$$

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

$$8b-b^{0}$$

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

$$8b-1$$