Solve D(292/3)^2quad(2)|99

$$D ( 29 \frac { 2 } { 3 } ) ^ { 2 } \quad ( 2 ) | 99$$

Evaluate

$$174262D$$

Solution Steps

Multiply 29 and 3 to get 87.

$$D\times \left(\frac{87+2}{3}\right)^{2}\times 2|99|$$

Add 87 and 2 to get 89.

$$D\times \left(\frac{89}{3}\right)^{2}\times 2|99|$$

Calculate \frac{89}{3} to the power of 2 and get \frac{7921}{9}.

$$D\times \frac{7921}{9}\times 2|99|$$

Multiply \frac{7921}{9} and 2 to get \frac{15842}{9}.

$$D\times \frac{15842}{9}|99|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 99 is 99.

$$D\times \frac{15842}{9}\times 99$$

Multiply \frac{15842}{9} and 99 to get 174262.

$$D\times 174262$$

Differentiate w.r.t. D

$$174262$$

Steps Using Definition of a Derivative

Multiply 29 and 3 to get 87.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \left(\frac{87+2}{3}\right)^{2}\times 2|99|)$$

Add 87 and 2 to get 89.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \left(\frac{89}{3}\right)^{2}\times 2|99|)$$

Calculate \frac{89}{3} to the power of 2 and get \frac{7921}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \frac{7921}{9}\times 2|99|)$$

Multiply \frac{7921}{9} and 2 to get \frac{15842}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \frac{15842}{9}|99|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 99 is 99.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \frac{15842}{9}\times 99)$$

Multiply \frac{15842}{9} and 99 to get 174262.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times 174262)$$

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

$$174262D^{1-1}$$

Subtract 1 from 1.

$$174262D^{0}$$

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

$$174262\times 1$$

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

$$174262$$