Solve 15C_{2}*0.6^2*0.40^13

$$15 C _ { 2 } * 0.6 ^ { 2 } * 0.40 ^ { 13 }$$

Evaluate

$$\frac{221184C_{2}}{6103515625}$$

Solution Steps

Calculate 0.6 to the power of 2 and get 0.36.

$$15C_{2}\times 0.36\times 0.4^{13}$$

Multiply 15 and 0.36 to get 5.4.

$$5.4C_{2}\times 0.4^{13}$$

Calculate 0.4 to the power of 13 and get 0.0000067108864.

$$5.4C_{2}\times 0.0000067108864$$

Multiply 5.4 and 0.0000067108864 to get 0.00003623878656.

$$0.00003623878656C_{2}$$

Differentiate w.r.t. C_2

$$0.00003623878656$$

Steps Using Definition of a Derivative

Calculate 0.6 to the power of 2 and get 0.36.

$$\frac{\mathrm{d}}{\mathrm{d}C_{2}}(15C_{2}\times 0.36\times 0.4^{13})$$

Multiply 15 and 0.36 to get 5.4.

$$\frac{\mathrm{d}}{\mathrm{d}C_{2}}(5.4C_{2}\times 0.4^{13})$$

Calculate 0.4 to the power of 13 and get 0.0000067108864.

$$\frac{\mathrm{d}}{\mathrm{d}C_{2}}(5.4C_{2}\times 0.0000067108864)$$

Multiply 5.4 and 0.0000067108864 to get 0.00003623878656.

$$\frac{\mathrm{d}}{\mathrm{d}C_{2}}(0.00003623878656C_{2})$$

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

$$0.00003623878656C_{2}^{1-1}$$

Subtract 1 from 1.

$$0.00003623878656C_{2}^{0}$$

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

$$0.00003623878656\times 1$$

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

$$0.00003623878656$$