Solve 44r^2(5.5)^2(4)

$$44 r ^ { 2 } ( 5.5 ) ^ { 2 } ( 4 )$$

Evaluate

$$5324r^{2}$$

Solution Steps

Calculate 5.5 to the power of 2 and get 30.25.

$$44r^{2}\times 30.25\times 4$$

Multiply 44 and 30.25 to get 1331.

$$1331r^{2}\times 4$$

Multiply 1331 and 4 to get 5324.

$$5324r^{2}$$

Differentiate w.r.t. r

$$10648r$$

Steps Using Definition of a Derivative

Calculate 5.5 to the power of 2 and get 30.25.

$$\frac{\mathrm{d}}{\mathrm{d}r}(44r^{2}\times 30.25\times 4)$$

Multiply 44 and 30.25 to get 1331.

$$\frac{\mathrm{d}}{\mathrm{d}r}(1331r^{2}\times 4)$$

Multiply 1331 and 4 to get 5324.

$$\frac{\mathrm{d}}{\mathrm{d}r}(5324r^{2})$$

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

$$2\times 5324r^{2-1}$$

Multiply 2 times 5324.

$$10648r^{2-1}$$

Subtract 1 from 2.

$$10648r^{1}$$

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

$$10648r$$