Solve 4rdiv16r^7*12r^4

$$4 r \div 16 r ^ { 7 } \times 12 r ^ { 4 }$$

Evaluate

$$3r^{12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{4r}{16}r^{11}\times 12$$

Divide 4r by 16 to get \frac{1}{4}r.

$$\frac{1}{4}rr^{11}\times 12$$

To multiply powers of the same base, add their exponents. Add 1 and 11 to get 12.

$$\frac{1}{4}r^{12}\times 12$$

Multiply \frac{1}{4} and 12 to get 3.

$$3r^{12}$$

Differentiate w.r.t. r

$$36r^{11}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 4 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4r}{16}r^{11}\times 12)$$

Divide 4r by 16 to get \frac{1}{4}r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{4}rr^{11}\times 12)$$

To multiply powers of the same base, add their exponents. Add 1 and 11 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{4}r^{12}\times 12)$$

Multiply \frac{1}{4} and 12 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}r}(3r^{12})$$

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

$$12\times 3r^{12-1}$$

Multiply 12 times 3.

$$36r^{12-1}$$

Subtract 1 from 12.

$$36r^{11}$$