Solve 6a^5(6a^5)

$$6 a ^ { 5 } ( 6 a ^ { 5 } )$$

Evaluate

$$36a^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$6a^{10}\times 6$$

Multiply 6 and 6 to get 36.

$$36a^{10}$$

Differentiate w.r.t. a

$$360a^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6a^{10}\times 6)$$

Multiply 6 and 6 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}a}(36a^{10})$$

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

$$10\times 36a^{10-1}$$

Multiply 10 times 36.

$$360a^{10-1}$$

Subtract 1 from 10.

$$360a^{9}$$