Solve 3/4Gamma_{15}div11/3}

$$\frac { 3 } { 4 } \Gamma _ { 15 } \div \frac { 11 } { 3 } \}$$

Evaluate

$$\frac{9\Gamma _{15}}{44}$$

Solution Steps

Divide \frac{3}{4}\Gamma _{15} by \frac{11}{3} by multiplying \frac{3}{4}\Gamma _{15} by the reciprocal of \frac{11}{3}.

$$\frac{\frac{3}{4}\Gamma _{15}\times 3}{11}$$

Express \frac{3}{4}\times 3 as a single fraction.

$$\frac{\frac{3\times 3}{4}\Gamma _{15}}{11}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{9}{4}\Gamma _{15}}{11}$$

Divide \frac{9}{4}\Gamma _{15} by 11 to get \frac{9}{44}\Gamma _{15}.

$$\frac{9}{44}\Gamma _{15}$$

Differentiate w.r.t. Γ_15

$$\frac{9}{44} = 0.20454545454545456$$

Steps Using Definition of a Derivative

Divide \frac{3}{4}\Gamma _{15} by \frac{11}{3} by multiplying \frac{3}{4}\Gamma _{15} by the reciprocal of \frac{11}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}\Gamma _{15}}(\frac{\frac{3}{4}\Gamma _{15}\times 3}{11})$$

Express \frac{3}{4}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}\Gamma _{15}}(\frac{\frac{3\times 3}{4}\Gamma _{15}}{11})$$

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}\Gamma _{15}}(\frac{\frac{9}{4}\Gamma _{15}}{11})$$

Divide \frac{9}{4}\Gamma _{15} by 11 to get \frac{9}{44}\Gamma _{15}.

$$\frac{\mathrm{d}}{\mathrm{d}\Gamma _{15}}(\frac{9}{44}\Gamma _{15})$$

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

$$\frac{9}{44}\Gamma _{15}^{1-1}$$

Subtract 1 from 1.

$$\frac{9}{44}\Gamma _{15}^{0}$$

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

$$\frac{9}{44}\times 1$$

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

$$\frac{9}{44}$$