Solve 27x^4:(-9x^3)*(-2x^2)=

$$27 x ^ { 4 } : ( - 9 x ^ { 3 } ) \cdot ( - 2 x ^ { 2 } ) =$$

Evaluate

$$6x^{3}$$

Solution Steps

Cancel out 9x^{3} in both numerator and denominator.

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

Anything divided by -1 gives its opposite.

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

Multiply -3 and -2 to get 6.

$$6xx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$6x^{3}$$

Differentiate w.r.t. x

$$18x^{2}$$

Steps Using Definition of a Derivative

Cancel out 9x^{3} in both numerator and denominator.

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

Anything divided by -1 gives its opposite.

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

Multiply -3 and -2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6xx^{2})$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3})$$

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

$$3\times 6x^{3-1}$$

Multiply 3 times 6.

$$18x^{3-1}$$

Subtract 1 from 3.

$$18x^{2}$$