Solve n3pi-cos3pi/2

$$n 3 \pi - \cos \frac { 3 \pi } { 2 }$$

Evaluate

$$\pi n_{3}$$

Solution Steps

Get the value of \cos(\frac{3\pi }{2}) from trigonometric values table.

$$n_{3}\pi -0$$

Multiply -1 and 0 to get 0.

$$n_{3}\pi +0$$

Anything plus zero gives itself.

$$n_{3}\pi$$

Differentiate w.r.t. n_3

$$\pi$$

Steps Using Definition of a Derivative

Get the value of \cos(\frac{3\pi }{2}) from trigonometric values table.

$$\frac{\mathrm{d}}{\mathrm{d}n_{3}}(n_{3}\pi -0)$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}n_{3}}(n_{3}\pi +0)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}n_{3}}(n_{3}\pi )$$

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

$$\pi n_{3}^{1-1}$$

Subtract 1 from 1.

$$\pi n_{3}^{0}$$

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

$$\pi \times 1$$

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

$$\pi$$