Solve -4n^53n^8

$$-4 { n }^{ 5 } 3 { n }^{ 8 }$$

Evaluate

$$-12n^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$-4n^{13}\times 3$$

Multiply -4 and 3 to get -12.

$$-12n^{13}$$

Differentiate w.r.t. n

$$-156n^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-4n^{13}\times 3)$$

Multiply -4 and 3 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-12n^{13})$$

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

$$13\left(-12\right)n^{13-1}$$

Multiply 13 times -12.

$$-156n^{13-1}$$

Subtract 1 from 13.

$$-156n^{12}$$