Solve (101.5)^2-(100.5)^2quadA

$$( 101.5 ) ^ { 2 } - ( 100.5 ) ^ { 2 } \quad A$$

Evaluate

$$\frac{41209-40401A}{4}$$

Solution Steps

Calculate 101.5 to the power of 2 and get 10302.25.

$$10302.25-100.5^{2}A$$

Calculate 100.5 to the power of 2 and get 10100.25.

$$10302.25-10100.25A$$

Differentiate w.r.t. A

$$-10100.25$$

Steps Using Derivative Rule for Sum

Calculate 101.5 to the power of 2 and get 10302.25.

$$\frac{\mathrm{d}}{\mathrm{d}A}(10302.25-100.5^{2}A)$$

Calculate 100.5 to the power of 2 and get 10100.25.

$$\frac{\mathrm{d}}{\mathrm{d}A}(10302.25-10100.25A)$$

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}.

$$-10100.25A^{1-1}$$

Subtract 1 from 1.

$$-10100.25A^{0}$$

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

$$-10100.25$$