Solve X13/122*102

$$\frac { X 13 } { 122 } \times 102$$

Evaluate

$$\frac{51X_{13}}{61}$$

Solution Steps

Express \frac{X_{13}}{122}\times 102 as a single fraction.

$$\frac{X_{13}\times 102}{122}$$

Divide X_{13}\times 102 by 122 to get X_{13}\times \frac{51}{61}.

$$X_{13}\times \frac{51}{61}$$

Differentiate w.r.t. X_13

$$\frac{51}{61} = 0.8360655737704918$$

Steps Using Definition of a Derivative

Express \frac{X_{13}}{122}\times 102 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}X_{13}}(\frac{X_{13}\times 102}{122})$$

Divide X_{13}\times 102 by 122 to get X_{13}\times \frac{51}{61}.

$$\frac{\mathrm{d}}{\mathrm{d}X_{13}}(X_{13}\times \frac{51}{61})$$

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

$$\frac{51}{61}X_{13}^{1-1}$$

Subtract 1 from 1.

$$\frac{51}{61}X_{13}^{0}$$

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

$$\frac{51}{61}\times 1$$

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

$$\frac{51}{61}$$