Solve 6a^6:2a^2=

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

Evaluate

$$3a^{8}$$

Solution Steps

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

$$3a^{6}a^{2}$$

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

$$3a^{8}$$

Differentiate w.r.t. a

$$24a^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{6}a^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a^{8})$$

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

$$8\times 3a^{8-1}$$

Multiply 8 times 3.

$$24a^{8-1}$$

Subtract 1 from 8.

$$24a^{7}$$