Solve 12a^6div3a^4

$$12 a ^ { 6 } \div 3 a ^ { 4 }$$

Evaluate

$$4a^{10}$$

Solution Steps

Divide 12a^{6} by 3 to get 4a^{6}.

$$4a^{6}a^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$4a^{10}$$

Differentiate w.r.t. a

$$40a^{9}$$

Steps Using Definition of a Derivative

Divide 12a^{6} by 3 to get 4a^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{6}a^{4})$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{10})$$

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

$$10\times 4a^{10-1}$$

Multiply 10 times 4.

$$40a^{10-1}$$

Subtract 1 from 10.

$$40a^{9}$$