Solve 4/62*4x*37

$$\frac{ 4 }{ 6 } 2 \times 4x \times 37$$

Evaluate

$$\frac{592x}{3}$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}\times 2\times 4x\times 37$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{2\times 2}{3}\times 4x\times 37$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}\times 4x\times 37$$

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

$$\frac{4\times 4}{3}x\times 37$$

Multiply 4 and 4 to get 16.

$$\frac{16}{3}x\times 37$$

Express \frac{16}{3}\times 37 as a single fraction.

$$\frac{16\times 37}{3}x$$

Multiply 16 and 37 to get 592.

$$\frac{592}{3}x$$

Differentiate w.r.t. x

$$\frac{592}{3} = 197\frac{1}{3} = 197.33333333333334$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}\times 2\times 4x\times 37)$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 2}{3}\times 4x\times 37)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{3}\times 4x\times 37)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 4}{3}x\times 37)$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{3}x\times 37)$$

Express \frac{16}{3}\times 37 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16\times 37}{3}x)$$

Multiply 16 and 37 to get 592.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{592}{3}x)$$

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

$$\frac{592}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{592}{3}x^{0}$$

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

$$\frac{592}{3}\times 1$$

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

$$\frac{592}{3}$$