Solve 2r^0*(2r^0)^2/r

$$\frac { 2 r ^ { 0 } \cdot ( 2 r ^ { 0 } ) ^ { 2 } } { r }$$

Evaluate

$$\frac{8}{r}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2\times \left(2r^{0}\right)^{2}}{r^{1}}$$

Calculate r to the power of 0 and get 1.

$$\frac{2\times \left(2\times 1\right)^{2}}{r^{1}}$$

Multiply 2 and 1 to get 2.

$$\frac{2\times 2^{2}}{r^{1}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2\times 4}{r^{1}}$$

Multiply 2 and 4 to get 8.

$$\frac{8}{r^{1}}$$

Calculate r to the power of 1 and get r.

$$\frac{8}{r}$$

Differentiate w.r.t. r

$$-\frac{8}{r^{2}}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2\times \left(2r^{0}\right)^{2}}{r^{1}})$$

Calculate r to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2\times \left(2\times 1\right)^{2}}{r^{1}})$$

Multiply 2 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2\times 2^{2}}{r^{1}})$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{2\times 4}{r^{1}})$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{8}{r^{1}})$$

Calculate r to the power of 1 and get r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{8}{r})$$

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

$$-8r^{-1-1}$$

Subtract 1 from -1.

$$-8r^{-2}$$