Solve 16a^6:2a=

$$16 a ^ { 6 } : 2 a =$$

Evaluate

$$8a^{7}$$

Solution Steps

Divide 16a^{6} by 2 to get 8a^{6}.

$$8a^{6}a$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$8a^{7}$$

Differentiate w.r.t. a

$$56a^{6}$$

Steps Using Definition of a Derivative

Divide 16a^{6} by 2 to get 8a^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{6}a)$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(8a^{7})$$

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

$$7\times 8a^{7-1}$$

Multiply 7 times 8.

$$56a^{7-1}$$

Subtract 1 from 7.

$$56a^{6}$$