Solve D|(-3/7)^2

$$D | ( - \frac { 3 } { 7 } ) ^ { 2 }$$

Evaluate

$$\frac{9D}{49}$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{7} is \frac{3}{7}.

$$D\times \left(\frac{3}{7}\right)^{2}$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$D\times \frac{9}{49}$$

Differentiate w.r.t. D

$$\frac{9}{49} = 0.1836734693877551$$

Steps Using Definition of a Derivative

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{7} is \frac{3}{7}.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \left(\frac{3}{7}\right)^{2})$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{\mathrm{d}}{\mathrm{d}D}(D\times \frac{9}{49})$$

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

$$\frac{9}{49}D^{1-1}$$

Subtract 1 from 1.

$$\frac{9}{49}D^{0}$$

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

$$\frac{9}{49}\times 1$$

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

$$\frac{9}{49}$$