Solve (-36x^4)div(-9x)*(-2)

$$( - 36 x ^ { 4 } ) \div ( - 9 x ) \cdot ( - 2 )$$

Evaluate

$$-8x^{3}$$

Solution Steps

Cancel out 9x in both numerator and denominator.

$$\frac{-4x^{3}}{-1}\left(-2\right)$$

Anything divided by -1 gives its opposite.

$$4x^{3}\left(-2\right)$$

Multiply 4 and -2 to get -8.

$$-8x^{3}$$

Differentiate w.r.t. x

$$-24x^{2}$$

Steps Using Definition of a Derivative

Cancel out 9x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-4x^{3}}{-1}\left(-2\right))$$

Anything divided by -1 gives its opposite.

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

Multiply 4 and -2 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8x^{3})$$

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

$$3\left(-8\right)x^{3-1}$$

Multiply 3 times -8.

$$-24x^{3-1}$$

Subtract 1 from 3.

$$-24x^{2}$$