Solve -68div16/11(-7a)

$$- 68 \div \frac { 16 } { 11 } ( - 7 a )$$

Evaluate

$$\frac{1309a}{4}$$

Solution Steps

Divide -68 by \frac{16}{11} by multiplying -68 by the reciprocal of \frac{16}{11}.

$$-68\times \frac{11}{16}\left(-7\right)a$$

Express -68\times \frac{11}{16} as a single fraction.

$$\frac{-68\times 11}{16}\left(-7\right)a$$

Multiply -68 and 11 to get -748.

$$\frac{-748}{16}\left(-7\right)a$$

Reduce the fraction \frac{-748}{16} to lowest terms by extracting and canceling out 4.

$$-\frac{187}{4}\left(-7\right)a$$

Express -\frac{187}{4}\left(-7\right) as a single fraction.

$$\frac{-187\left(-7\right)}{4}a$$

Multiply -187 and -7 to get 1309.

$$\frac{1309}{4}a$$

Differentiate w.r.t. a

$$\frac{1309}{4} = 327\frac{1}{4} = 327.25$$

Steps Using Definition of a Derivative

Divide -68 by \frac{16}{11} by multiplying -68 by the reciprocal of \frac{16}{11}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-68\times \frac{11}{16}\left(-7\right)a)$$

Express -68\times \frac{11}{16} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-68\times 11}{16}\left(-7\right)a)$$

Multiply -68 and 11 to get -748.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-748}{16}\left(-7\right)a)$$

Reduce the fraction \frac{-748}{16} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{187}{4}\left(-7\right)a)$$

Express -\frac{187}{4}\left(-7\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-187\left(-7\right)}{4}a)$$

Multiply -187 and -7 to get 1309.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1309}{4}a)$$

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

$$\frac{1309}{4}a^{1-1}$$

Subtract 1 from 1.

$$\frac{1309}{4}a^{0}$$

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

$$\frac{1309}{4}\times 1$$

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

$$\frac{1309}{4}$$