Solve 12C_{3}(0.29)^3(0.71)^9

$$12 C _ { 3 } ( 0.29 ) ^ { 3 } ( 0.71 ) ^ { 9 }$$

Evaluate

$$\frac{3354597252066760251177C_{3}}{250000000000000000000000}$$

Solution Steps

Calculate 0.29 to the power of 3 and get 0.024389.

$$12C_{3}\times 0.024389\times 0.71^{9}$$

Multiply 12 and 0.024389 to get 0.292668.

$$0.292668C_{3}\times 0.71^{9}$$

Calculate 0.71 to the power of 9 and get 0.045848500718449031.

$$0.292668C_{3}\times 0.045848500718449031$$

Multiply 0.292668 and 0.045848500718449031 to get 0.013418389008267041004708.

$$0.013418389008267041004708C_{3}$$

Differentiate w.r.t. C_3

$$0.013418389008267041004708$$

Steps Using Definition of a Derivative

Calculate 0.29 to the power of 3 and get 0.024389.

$$\frac{\mathrm{d}}{\mathrm{d}C_{3}}(12C_{3}\times 0.024389\times 0.71^{9})$$

Multiply 12 and 0.024389 to get 0.292668.

$$\frac{\mathrm{d}}{\mathrm{d}C_{3}}(0.292668C_{3}\times 0.71^{9})$$

Calculate 0.71 to the power of 9 and get 0.045848500718449031.

$$\frac{\mathrm{d}}{\mathrm{d}C_{3}}(0.292668C_{3}\times 0.045848500718449031)$$

Multiply 0.292668 and 0.045848500718449031 to get 0.013418389008267041004708.

$$\frac{\mathrm{d}}{\mathrm{d}C_{3}}(0.013418389008267041004708C_{3})$$

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

$$0.013418389008267041004708C_{3}^{1-1}$$

Subtract 1 from 1.

$$0.013418389008267041004708C_{3}^{0}$$

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

$$0.013418389008267041004708\times 1$$

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

$$0.013418389008267041004708$$