Solve r^55^6-r^55^12=

$$r ^ { 5 } 5 ^ { 6 } - r ^ { 5 } 5 ^ { 12 } =$$

Evaluate

$$-244125000r^{5}$$

Solution Steps

Calculate 5 to the power of 6 and get 15625.

$$r^{5}\times 15625-r^{5}\times 5^{12}$$

Calculate 5 to the power of 12 and get 244140625.

$$r^{5}\times 15625-r^{5}\times 244140625$$

Combine r^{5}\times 15625 and -r^{5}\times 244140625 to get -244125000r^{5}.

$$-244125000r^{5}$$

Differentiate w.r.t. r

$$-1220625000r^{4}$$

Steps Using Definition of a Derivative

Calculate 5 to the power of 6 and get 15625.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{5}\times 15625-r^{5}\times 5^{12})$$

Calculate 5 to the power of 12 and get 244140625.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{5}\times 15625-r^{5}\times 244140625)$$

Combine r^{5}\times 15625 and -r^{5}\times 244140625 to get -244125000r^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(-244125000r^{5})$$

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

$$5\left(-244125000\right)r^{5-1}$$

Multiply 5 times -244125000.

$$-1220625000r^{5-1}$$

Subtract 1 from 5.

$$-1220625000r^{4}$$