Solve =A500+(15/100*1500)

$$= A 500 + ( \frac { 15 } { 100 } \times 1500 )$$

Evaluate

$$A_{500}+225$$

Solution Steps

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$A_{500}+\frac{3}{20}\times 1500$$

Express \frac{3}{20}\times 1500 as a single fraction.

$$A_{500}+\frac{3\times 1500}{20}$$

Multiply 3 and 1500 to get 4500.

$$A_{500}+\frac{4500}{20}$$

Divide 4500 by 20 to get 225.

$$A_{500}+225$$

Differentiate w.r.t. A_500

$$1$$

Steps Using Derivative Rule for Sum

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}A_{500}}(A_{500}+\frac{3}{20}\times 1500)$$

Express \frac{3}{20}\times 1500 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}A_{500}}(A_{500}+\frac{3\times 1500}{20})$$

Multiply 3 and 1500 to get 4500.

$$\frac{\mathrm{d}}{\mathrm{d}A_{500}}(A_{500}+\frac{4500}{20})$$

Divide 4500 by 20 to get 225.

$$\frac{\mathrm{d}}{\mathrm{d}A_{500}}(A_{500}+225)$$

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}.

$$A_{500}^{1-1}$$

Subtract 1 from 1.

$$A_{500}^{0}$$

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

$$1$$