Solve 90^2-120b+4b^2-9

$$90 ^ { 2 } - 120 b + 4 b ^ { 2 } - 9$$

Evaluate

$$4b^{2}-120b+8091$$

Solution Steps

Calculate 90 to the power of 2 and get 8100.

$$8100-120b+4b^{2}-9$$

Subtract 9 from 8100 to get 8091.

$$8091-120b+4b^{2}$$

Differentiate w.r.t. b

$$8\left(b-15\right)$$

Steps Using Derivative Rule for Sum

Calculate 90 to the power of 2 and get 8100.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8100-120b+4b^{2}-9)$$

Subtract 9 from 8100 to get 8091.

$$\frac{\mathrm{d}}{\mathrm{d}b}(8091-120b+4b^{2})$$

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}.

$$-120b^{1-1}+2\times 4b^{2-1}$$

Subtract 1 from 1.

$$-120b^{0}+2\times 4b^{2-1}$$

Multiply 2 times 4.

$$-120b^{0}+8b^{2-1}$$

Subtract 1 from 2.

$$-120b^{0}+8b^{1}$$

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

$$-120b^{0}+8b$$

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

$$-120+8b$$