Solve 8x/(8-3)!*3!*5!*7

$$\frac { 8 x } { ( 8 - 3 ) ! \cdot 3 ! } \cdot 5 ! \cdot 7$$

Evaluate

$$\frac{28x}{3}$$

Solution Steps

Subtract 3 from 8 to get 5.

$$\frac{8x}{5!\times 3!}\times 5!\times 7$$

The factorial of 5 is 120.

$$\frac{8x}{120\times 3!}\times 5!\times 7$$

The factorial of 3 is 6.

$$\frac{8x}{120\times 6}\times 5!\times 7$$

Multiply 120 and 6 to get 720.

$$\frac{8x}{720}\times 5!\times 7$$

Divide 8x by 720 to get \frac{1}{90}x.

$$\frac{1}{90}x\times 5!\times 7$$

The factorial of 5 is 120.

$$\frac{1}{90}x\times 120\times 7$$

Multiply \frac{1}{90} and 120 to get \frac{120}{90}.

$$\frac{120}{90}x\times 7$$

Reduce the fraction \frac{120}{90} to lowest terms by extracting and canceling out 30.

$$\frac{4}{3}x\times 7$$

Express \frac{4}{3}\times 7 as a single fraction.

$$\frac{4\times 7}{3}x$$

Multiply 4 and 7 to get 28.

$$\frac{28}{3}x$$

Differentiate w.r.t. x

$$\frac{28}{3} = 9\frac{1}{3} = 9.333333333333334$$

Steps Using Definition of a Derivative

Subtract 3 from 8 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x}{5!\times 3!}\times 5!\times 7)$$

The factorial of 5 is 120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x}{120\times 3!}\times 5!\times 7)$$

The factorial of 3 is 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x}{120\times 6}\times 5!\times 7)$$

Multiply 120 and 6 to get 720.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x}{720}\times 5!\times 7)$$

Divide 8x by 720 to get \frac{1}{90}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{90}x\times 5!\times 7)$$

The factorial of 5 is 120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{90}x\times 120\times 7)$$

Multiply \frac{1}{90} and 120 to get \frac{120}{90}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{120}{90}x\times 7)$$

Reduce the fraction \frac{120}{90} to lowest terms by extracting and canceling out 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{3}x\times 7)$$

Express \frac{4}{3}\times 7 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 7}{3}x)$$

Multiply 4 and 7 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{28}{3}x)$$

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

$$\frac{28}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{28}{3}x^{0}$$

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

$$\frac{28}{3}\times 1$$

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

$$\frac{28}{3}$$