Solve 44r^2(55)^2(4)

$$44 r ^ { 2 } ( 55 ) ^ { 2 } ( 4 )$$

Evaluate

$$532400r^{2}$$

Solution Steps

Calculate 55 to the power of 2 and get 3025.

$$44r^{2}\times 3025\times 4$$

Multiply 44 and 3025 to get 133100.

$$133100r^{2}\times 4$$

Multiply 133100 and 4 to get 532400.

$$532400r^{2}$$

Differentiate w.r.t. r

$$1064800r$$

Steps Using Definition of a Derivative

Calculate 55 to the power of 2 and get 3025.

$$\frac{\mathrm{d}}{\mathrm{d}r}(44r^{2}\times 3025\times 4)$$

Multiply 44 and 3025 to get 133100.

$$\frac{\mathrm{d}}{\mathrm{d}r}(133100r^{2}\times 4)$$

Multiply 133100 and 4 to get 532400.

$$\frac{\mathrm{d}}{\mathrm{d}r}(532400r^{2})$$

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

$$2\times 532400r^{2-1}$$

Multiply 2 times 532400.

$$1064800r^{2-1}$$

Subtract 1 from 2.

$$1064800r^{1}$$

For any term t, t^{1}=t.

$$1064800r$$