Solve C(2,0)+C(2,1)+C(2,2)

$$C ( 2,0 ) + C ( 2,1 ) + C ( 2,2 )$$

Evaluate

$$\frac{63C}{10}$$

Solution Steps

Combine C\times 2 and C\times 2,1 to get 4,1C.

$$4,1C+C\times 2,2$$

Combine 4,1C and C\times 2,2 to get 6,3C.

$$6,3C$$

Differentiate w.r.t. C

$$6,3$$

Steps Using Definition of a Derivative

Combine C\times 2 and C\times 2,1 to get 4,1C.

$$\frac{\mathrm{d}}{\mathrm{d}C}(4,1C+C\times 2,2)$$

Combine 4,1C and C\times 2,2 to get 6,3C.

$$\frac{\mathrm{d}}{\mathrm{d}C}(6,3C)$$

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

$$6,3C^{1-1}$$

Subtract 1 from 1.

$$6,3C^{0}$$

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

$$6,3\times 1$$

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

$$6,3$$