Solve (6x^3)(4x)/-12x^10

$$\frac { ( 6 x ^ { 3 } ) ( 4 x ) } { - 12 x ^ { 10 } }$$

Evaluate

$$-\frac{2}{x^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{6x^{4}\times 4}{-12x^{10}}$$

Cancel out 2\times 6x^{4} in both numerator and denominator.

$$\frac{2}{-x^{6}}$$

Differentiate w.r.t. x

$$\frac{12}{x^{7}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x}{-12}x^{3-10})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-2x\right)x^{-7})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-7\left(-2x\right)x^{-7-1}$$

Do the arithmetic.

$$14xx^{-8}$$