Solve f(2pi)-f(3pi/2)/2pi-frac{3pi{2}}

$$\frac { f ( 2 \pi ) - f ( \frac { 3 \pi } { 2 } ) } { 2 \pi - \frac { 3 \pi } { 2 } }$$

Evaluate

$$f$$

Short Solution Steps

Express f\times \frac{3\pi }{2} as a single fraction.

$$\frac{f\times 2\pi -\frac{f\times 3\pi }{2}}{2\pi -\frac{3\pi }{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply f\times 2\pi times \frac{2}{2}.

$$\frac{\frac{2f\times 2\pi }{2}-\frac{f\times 3\pi }{2}}{2\pi -\frac{3\pi }{2}}$$

Since \frac{2f\times 2\pi }{2} and \frac{f\times 3\pi }{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2f\times 2\pi -f\times 3\pi }{2}}{2\pi -\frac{3\pi }{2}}$$

Do the multiplications in 2f\times 2\pi -f\times 3\pi .

$$\frac{\frac{4f\pi -3f\pi }{2}}{2\pi -\frac{3\pi }{2}}$$

Combine like terms in 4f\pi -3f\pi .

$$\frac{\frac{f\pi }{2}}{2\pi -\frac{3\pi }{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\pi times \frac{2}{2}.

$$\frac{\frac{f\pi }{2}}{\frac{2\times 2\pi }{2}-\frac{3\pi }{2}}$$

Since \frac{2\times 2\pi }{2} and \frac{3\pi }{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{f\pi }{2}}{\frac{2\times 2\pi -3\pi }{2}}$$

Do the multiplications in 2\times 2\pi -3\pi .

$$\frac{\frac{f\pi }{2}}{\frac{4\pi -3\pi }{2}}$$

Combine like terms in 4\pi -3\pi .

$$\frac{\frac{f\pi }{2}}{\frac{\pi }{2}}$$

Divide \frac{f\pi }{2} by \frac{\pi }{2} by multiplying \frac{f\pi }{2} by the reciprocal of \frac{\pi }{2}.

$$\frac{f\pi \times 2}{2\pi }$$

Cancel out 2\pi in both numerator and denominator.

$$f$$

Differentiate w.r.t. f

$$1$$

Steps Using Definition of a Derivative

Express f\times \frac{3\pi }{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f\times 2\pi -\frac{f\times 3\pi }{2}}{2\pi -\frac{3\pi }{2}})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply f\times 2\pi times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{2f\times 2\pi }{2}-\frac{f\times 3\pi }{2}}{2\pi -\frac{3\pi }{2}})$$

Since \frac{2f\times 2\pi }{2} and \frac{f\times 3\pi }{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{2f\times 2\pi -f\times 3\pi }{2}}{2\pi -\frac{3\pi }{2}})$$

Do the multiplications in 2f\times 2\pi -f\times 3\pi .

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{4f\pi -3f\pi }{2}}{2\pi -\frac{3\pi }{2}})$$

Combine like terms in 4f\pi -3f\pi .

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{f\pi }{2}}{2\pi -\frac{3\pi }{2}})$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\pi times \frac{2}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{f\pi }{2}}{\frac{2\times 2\pi }{2}-\frac{3\pi }{2}})$$

Since \frac{2\times 2\pi }{2} and \frac{3\pi }{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{f\pi }{2}}{\frac{2\times 2\pi -3\pi }{2}})$$

Do the multiplications in 2\times 2\pi -3\pi .

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{f\pi }{2}}{\frac{4\pi -3\pi }{2}})$$

Combine like terms in 4\pi -3\pi .

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{\frac{f\pi }{2}}{\frac{\pi }{2}})$$

Divide \frac{f\pi }{2} by \frac{\pi }{2} by multiplying \frac{f\pi }{2} by the reciprocal of \frac{\pi }{2}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f\pi \times 2}{2\pi })$$

Cancel out 2\pi in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f)$$

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

$$f^{1-1}$$

Subtract 1 from 1.

$$f^{0}$$

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

$$1$$