Solve 2n^4*6n^4

$$2 n ^ { 4 } * 6 n ^ { 4 }$$

Evaluate

$$12n^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$2n^{8}\times 6$$

Multiply 2 and 6 to get 12.

$$12n^{8}$$

Differentiate w.r.t. n

$$96n^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}n}(2n^{8}\times 6)$$

Multiply 2 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}n}(12n^{8})$$

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

$$8\times 12n^{8-1}$$

Multiply 8 times 12.

$$96n^{8-1}$$

Subtract 1 from 8.

$$96n^{7}$$