Solve 2N^4*5N^4

$$2 N ^ { 4 } \times 5 N ^ { 4 }$$

Evaluate

$$10N^{8}$$

Solution Steps

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

$$2N^{8}\times 5$$

Multiply 2 and 5 to get 10.

$$10N^{8}$$

Differentiate w.r.t. N

$$80N^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}N}(2N^{8}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}N}(10N^{8})$$

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

$$8\times 10N^{8-1}$$

Multiply 8 times 10.

$$80N^{8-1}$$

Subtract 1 from 8.

$$80N^{7}$$