Solve -20abc(-1/5ab)

$$- 20 a b c ( - \frac { 1 } { 5 a b } )$$

Evaluate

$$4c$$

Solution Steps

Multiply -20 and -1 to get 20.

$$20abc\times \frac{1}{5ab}$$

Express a\times \frac{1}{5ab} as a single fraction.

$$20\times \frac{a}{5ab}bc$$

Cancel out a in both numerator and denominator.

$$20\times \frac{1}{5b}bc$$

Express 20\times \frac{1}{5b} as a single fraction.

$$\frac{20}{5b}bc$$

Express \frac{20}{5b}b as a single fraction.

$$\frac{20b}{5b}c$$

Cancel out 5b in both numerator and denominator.

$$4c$$

Differentiate w.r.t. c

$$4$$

Steps Using Definition of a Derivative

Multiply -20 and -1 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}c}(20abc\times \frac{1}{5ab})$$

Express a\times \frac{1}{5ab} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}c}(20\times \frac{a}{5ab}bc)$$

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(20\times \frac{1}{5b}bc)$$

Express 20\times \frac{1}{5b} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{20}{5b}bc)$$

Express \frac{20}{5b}b as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{20b}{5b}c)$$

Cancel out 5b in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}c}(4c)$$

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

$$4c^{1-1}$$

Subtract 1 from 1.

$$4c^{0}$$

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

$$4\times 1$$

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

$$4$$