Solve (-36x^4)div(-8x)*(-2)

$$( - 36 x ^ { 4 } ) \div ( - 8 x ) \cdot ( - 2 )$$

Evaluate

$$-9x^{3}$$

Solution Steps

Cancel out 4x in both numerator and denominator.

$$\frac{-9x^{3}}{-2}\left(-2\right)$$

Express \frac{-9x^{3}}{-2}\left(-2\right) as a single fraction.

$$\frac{-\left(-9\right)x^{3}\times 2}{-2}$$

Cancel out -2 and -2.

$$-\left(-9\right)x^{3}\left(-1\right)$$

Multiply -1 and -9 to get 9.

$$9x^{3}\left(-1\right)$$

Multiply 9 and -1 to get -9.

$$-9x^{3}$$

Differentiate w.r.t. x

$$-27x^{2}$$

Steps Using Definition of a Derivative

Cancel out 4x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-9x^{3}}{-2}\left(-2\right))$$

Express \frac{-9x^{3}}{-2}\left(-2\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\left(-9\right)x^{3}\times 2}{-2})$$

Cancel out -2 and -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(-9\right)x^{3}\left(-1\right))$$

Multiply -1 and -9 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{3}\left(-1\right))$$

Multiply 9 and -1 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{3})$$

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

$$3\left(-9\right)x^{3-1}$$

Multiply 3 times -9.

$$-27x^{3-1}$$

Subtract 1 from 3.

$$-27x^{2}$$