Solve 2+2ab-4b^2+5

$$2 + 2 a b - 4 b ^ { 2 } + 5$$

Differentiate w.r.t. b

$$2\left(a-4b\right)$$

Steps Using Derivative Rule for Sum

Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}b}(7+2ab-4b^{2})$$

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}.

$$2\left(-4\right)b^{2-1}+2ab^{1-1}$$

Multiply 2 times -4.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$-8b^{1}+2ab^{0}$$

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

$$-8b+2ab^{0}$$

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

$$-8b+2a\times 1$$

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

$$-8b+2a$$

Evaluate

$$2ab-4b^{2}+7$$

Solution Steps

Add 2 and 5 to get 7.

$$7+2ab-4b^{2}$$