Solve a+2b+2b+4c-a-6b-4c+10b

$$a+2b+2b+4c-a-6b-4c+10b$$

Evaluate

$$8b$$

Solution Steps

Combine 2b and 2b to get 4b.

$$a+4b+4c-a-6b-4c+10b$$

Combine a and -a to get 0.

$$4b+4c-6b-4c+10b$$

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

$$-2b+4c-4c+10b$$

Combine 4c and -4c to get 0.

$$-2b+10b$$

Combine -2b and 10b to get 8b.

$$8b$$

Differentiate w.r.t. b

$$8$$

Steps Using Definition of a Derivative

Combine 2b and 2b to get 4b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(a+4b+4c-a-6b-4c+10b)$$

Combine a and -a to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b+4c-6b-4c+10b)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(-2b+4c-4c+10b)$$

Combine 4c and -4c to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-2b+10b)$$

Combine -2b and 10b to get 8b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8b)$$

The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from 1.

$$8b^{0}$$

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

$$8\times 1$$

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

$$8$$