Solve 6a^4div2a^2

$$6 a ^ { 4 } \div 2 a ^ { 2 }$$

Evaluate

$$3a^{6}$$

Solution Steps

Divide 6a^{4} by 2 to get 3a^{4}.

$$3a^{4}a^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$3a^{6}$$

Differentiate w.r.t. a

$$18a^{5}$$

Steps Using Definition of a Derivative

Divide 6a^{4} by 2 to get 3a^{4}.

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

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

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

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

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

Multiply 6 times 3.

$$18a^{6-1}$$

Subtract 1 from 6.

$$18a^{5}$$