Solve 18a/7*14a^6/3

$$\frac { 18 a } { 7 } \cdot \frac { 14 a ^ { 6 } } { 3 }$$

Evaluate

$$12a^{7}$$

Solution Steps

Multiply \frac{18a}{7} times \frac{14a^{6}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18a\times 14a^{6}}{7\times 3}$$

Cancel out 3\times 7 in both numerator and denominator.

$$2\times 6aa^{6}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$2\times 6a^{7}$$

Multiply 2 and 6 to get 12.

$$12a^{7}$$

Differentiate w.r.t. a

$$84a^{6}$$

Steps Using Definition of a Derivative

Multiply \frac{18a}{7} times \frac{14a^{6}}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{18a\times 14a^{6}}{7\times 3})$$

Cancel out 3\times 7 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2\times 6aa^{6})$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2\times 6a^{7})$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(12a^{7})$$

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

$$7\times 12a^{7-1}$$

Multiply 7 times 12.

$$84a^{7-1}$$

Subtract 1 from 7.

$$84a^{6}$$