Solve -2n^6*7n^3

$$- 2 n ^ { 6 } \cdot 7 n ^ { 3 }$$

Evaluate

$$-14n^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-2n^{9}\times 7$$

Multiply -2 and 7 to get -14.

$$-14n^{9}$$

Differentiate w.r.t. n

$$-126n^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-2n^{9}\times 7)$$

Multiply -2 and 7 to get -14.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-14n^{9})$$

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

$$9\left(-14\right)n^{9-1}$$

Multiply 9 times -14.

$$-126n^{9-1}$$

Subtract 1 from 9.

$$-126n^{8}$$