Solve 7/3*-2(5x*4)

$$\frac{ 7 }{ 3 } \times -2(5x \times 4)$$

Evaluate

$$-\frac{280x}{3}$$

Solution Steps

Express \frac{7}{3}\left(-2\right) as a single fraction.

$$\frac{7\left(-2\right)}{3}\times 5x\times 4$$

Multiply 7 and -2 to get -14.

$$\frac{-14}{3}\times 5x\times 4$$

Fraction \frac{-14}{3} can be rewritten as -\frac{14}{3} by extracting the negative sign.

$$-\frac{14}{3}\times 5x\times 4$$

Express -\frac{14}{3}\times 5 as a single fraction.

$$\frac{-14\times 5}{3}x\times 4$$

Multiply -14 and 5 to get -70.

$$\frac{-70}{3}x\times 4$$

Fraction \frac{-70}{3} can be rewritten as -\frac{70}{3} by extracting the negative sign.

$$-\frac{70}{3}x\times 4$$

Express -\frac{70}{3}\times 4 as a single fraction.

$$\frac{-70\times 4}{3}x$$

Multiply -70 and 4 to get -280.

$$\frac{-280}{3}x$$

Fraction \frac{-280}{3} can be rewritten as -\frac{280}{3} by extracting the negative sign.

$$-\frac{280}{3}x$$

Differentiate w.r.t. x

$$-\frac{280}{3} = -93\frac{1}{3} = -93.33333333333333$$

Steps Using Definition of a Derivative

Express \frac{7}{3}\left(-2\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7\left(-2\right)}{3}\times 5x\times 4)$$

Multiply 7 and -2 to get -14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-14}{3}\times 5x\times 4)$$

Fraction \frac{-14}{3} can be rewritten as -\frac{14}{3} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{14}{3}\times 5x\times 4)$$

Express -\frac{14}{3}\times 5 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-14\times 5}{3}x\times 4)$$

Multiply -14 and 5 to get -70.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-70}{3}x\times 4)$$

Fraction \frac{-70}{3} can be rewritten as -\frac{70}{3} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{70}{3}x\times 4)$$

Express -\frac{70}{3}\times 4 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-70\times 4}{3}x)$$

Multiply -70 and 4 to get -280.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-280}{3}x)$$

Fraction \frac{-280}{3} can be rewritten as -\frac{280}{3} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{280}{3}x)$$

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

$$-\frac{280}{3}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{280}{3}x^{0}$$

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

$$-\frac{280}{3}$$