Solve 4a^3:10a^4=

$$4 a ^ { 3 } : 10 a ^ { 4 } =$$

Evaluate

$$\frac{2a^{7}}{5}$$

Solution Steps

Divide 4a^{3} by 10 to get \frac{2}{5}a^{3}.

$$\frac{2}{5}a^{3}a^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{2}{5}a^{7}$$

Differentiate w.r.t. a

$$\frac{14a^{6}}{5}$$

Steps Using Definition of a Derivative

Divide 4a^{3} by 10 to get \frac{2}{5}a^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{5}a^{3}a^{4})$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2}{5}a^{7})$$

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

$$7\times \frac{2}{5}a^{7-1}$$

Multiply 7 times \frac{2}{5}.

$$\frac{14}{5}a^{7-1}$$

Subtract 1 from 7.

$$\frac{14}{5}a^{6}$$