Solve 4a^6div2a^2

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

Evaluate

$$2a^{8}$$

Solution Steps

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

$$2a^{6}a^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$2a^{8}$$

Differentiate w.r.t. a

$$16a^{7}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{8})$$

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

$$8\times 2a^{8-1}$$

Multiply 8 times 2.

$$16a^{8-1}$$

Subtract 1 from 8.

$$16a^{7}$$