Solve 10a^5:15a=

$$10 a ^ { 5 } : 15 a =$$

Evaluate

$$\frac{2a^{6}}{3}$$

Solution Steps

Divide 10a^{5} by 15 to get \frac{2}{3}a^{5}.

$$\frac{2}{3}a^{5}a$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{2}{3}a^{6}$$

Differentiate w.r.t. a

$$4a^{5}$$

Steps Using Definition of a Derivative

Divide 10a^{5} by 15 to get \frac{2}{3}a^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{3}a^{5}a)$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{3}a^{6})$$

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

$$6\times \frac{2}{3}a^{6-1}$$

Multiply 6 times \frac{2}{3}.

$$4a^{6-1}$$

Subtract 1 from 6.

$$4a^{5}$$