Solve 45/360*2*22/2x

$$\frac { 45 } { 360 } \times 2 \times \frac { 22 } { 2 } x$$

Evaluate

$$\frac{11x}{4}$$

Solution Steps

Reduce the fraction \frac{45}{360} to lowest terms by extracting and canceling out 45.

$$\frac{1}{8}\times 2\times \frac{22}{2}x$$

Multiply \frac{1}{8} and 2 to get \frac{2}{8}.

$$\frac{2}{8}\times \frac{22}{2}x$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\times \frac{22}{2}x$$

Divide 22 by 2 to get 11.

$$\frac{1}{4}\times 11x$$

Multiply \frac{1}{4} and 11 to get \frac{11}{4}.

$$\frac{11}{4}x$$

Differentiate w.r.t. x

$$\frac{11}{4} = 2\frac{3}{4} = 2.75$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{45}{360} to lowest terms by extracting and canceling out 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{8}\times 2\times \frac{22}{2}x)$$

Multiply \frac{1}{8} and 2 to get \frac{2}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{8}\times \frac{22}{2}x)$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}\times \frac{22}{2}x)$$

Divide 22 by 2 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}\times 11x)$$

Multiply \frac{1}{4} and 11 to get \frac{11}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11}{4}x)$$

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

$$\frac{11}{4}x^{1-1}$$

Subtract 1 from 1.

$$\frac{11}{4}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{11}{4}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{11}{4}$$