Solve 1/2|13|(6/k)

$$\frac { 1 } { 2 } | 13 | ( \frac { 6 } { k } )$$

Evaluate

$$\frac{39}{k}$$

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 13 is 13.

$$\frac{1}{2}\times 13\times \frac{6}{k}$$

Multiply \frac{1}{2} and 13 to get \frac{13}{2}.

$$\frac{13}{2}\times \frac{6}{k}$$

Multiply \frac{13}{2} times \frac{6}{k} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 6}{2k}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 13}{k}$$

Multiply 3 and 13 to get 39.

$$\frac{39}{k}$$

Differentiate w.r.t. k

$$-\frac{39}{k^{2}}$$

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 13 is 13.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{1}{2}\times 13\times \frac{6}{k})$$

Multiply \frac{1}{2} and 13 to get \frac{13}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{13}{2}\times \frac{6}{k})$$

Multiply \frac{13}{2} times \frac{6}{k} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{13\times 6}{2k})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{3\times 13}{k})$$

Multiply 3 and 13 to get 39.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{39}{k})$$

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

$$-39k^{-1-1}$$

Subtract 1 from -1.

$$-39k^{-2}$$