Solve 3n^5*4n^5

$$3 n ^ { 5 } \cdot 4 n ^ { 5 }$$

Evaluate

$$12n^{10}$$

Solution Steps

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

$$3n^{10}\times 4$$

Multiply 3 and 4 to get 12.

$$12n^{10}$$

Differentiate w.r.t. n

$$120n^{9}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(3n^{10}\times 4)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}n}(12n^{10})$$

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

$$10\times 12n^{10-1}$$

Multiply 10 times 12.

$$120n^{10-1}$$

Subtract 1 from 10.

$$120n^{9}$$