Solve n^4*2n^2*n^5

$$n^4 \cdot 2n^2 \cdot n^5$$

Evaluate

$$2n^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$n^{6}\times 2n^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$n^{11}\times 2$$

Differentiate w.r.t. n

$$22n^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{6}\times 2n^{5})$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{11}\times 2)$$

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

$$11\times 2n^{11-1}$$

Multiply 11 times 2.

$$22n^{11-1}$$

Subtract 1 from 11.

$$22n^{10}$$