Solve 54r^79r^6

$$54 r ^ { 7 } 9 r ^ { 6 }$$

Evaluate

$$486r^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$54r^{13}\times 9$$

Multiply 54 and 9 to get 486.

$$486r^{13}$$

Differentiate w.r.t. r

$$6318r^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}r}(54r^{13}\times 9)$$

Multiply 54 and 9 to get 486.

$$\frac{\mathrm{d}}{\mathrm{d}r}(486r^{13})$$

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

$$13\times 486r^{13-1}$$

Multiply 13 times 486.

$$6318r^{13-1}$$

Subtract 1 from 13.

$$6318r^{12}$$