Solve 3n^5*5n^10

$$3 n ^ { 5 } \cdot 5 n ^ { 10 }$$

Evaluate

$$15n^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 10 to get 15.

$$3n^{15}\times 5$$

Multiply 3 and 5 to get 15.

$$15n^{15}$$

Differentiate w.r.t. n

$$225n^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 10 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}n}(3n^{15}\times 5)$$

Multiply 3 and 5 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}n}(15n^{15})$$

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

$$15\times 15n^{15-1}$$

Multiply 15 times 15.

$$225n^{15-1}$$

Subtract 1 from 15.

$$225n^{14}$$