Solve 3a^8/xdiva/x

$$\frac { 3 a ^ { 8 } } { x } \div \frac { a } { x }$$

Evaluate

$$3a^{7}$$

Solution Steps

Divide \frac{3a^{8}}{x} by \frac{a}{x} by multiplying \frac{3a^{8}}{x} by the reciprocal of \frac{a}{x}.

$$\frac{3a^{8}x}{xa}$$

Cancel out ax in both numerator and denominator.

$$3a^{7}$$

Differentiate w.r.t. a

$$21a^{6}$$

Steps Using Definition of a Derivative

Divide \frac{3a^{8}}{x} by \frac{a}{x} by multiplying \frac{3a^{8}}{x} by the reciprocal of \frac{a}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3a^{8}x}{xa})$$

Cancel out ax in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{7})$$

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

$$7\times 3a^{7-1}$$

Multiply 7 times 3.

$$21a^{7-1}$$

Subtract 1 from 7.

$$21a^{6}$$