Solve a|-6a/11a

$$a | - \frac { 6 a } { 11 a }$$

Evaluate

$$\frac{6a}{11}$$

Solution Steps

Cancel out a in both numerator and denominator.

$$a|-\frac{6}{11}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{6}{11} is \frac{6}{11}.

$$a\times \frac{6}{11}$$

Differentiate w.r.t. a

$$\frac{6}{11} = 0.5454545454545454$$

Steps Using Definition of a Derivative

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|-\frac{6}{11}|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{6}{11} is \frac{6}{11}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times \frac{6}{11})$$

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

$$\frac{6}{11}a^{1-1}$$

Subtract 1 from 1.

$$\frac{6}{11}a^{0}$$

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

$$\frac{6}{11}\times 1$$

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

$$\frac{6}{11}$$