Solve 6u^5v^4/-2uv

$$\frac { 6 u ^ { 5 } v ^ { 4 } } { - 2 u v }$$

Evaluate

$$-3v^{3}u^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}u^{5}v^{4}}{\left(-2\right)^{1}u^{1}v^{1}}$$

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

$$\frac{6^{1}}{\left(-2\right)^{1}}u^{5-1}v^{4-1}$$

Subtract 1 from 5.

$$\frac{6^{1}}{\left(-2\right)^{1}}u^{4}v^{4-1}$$

Subtract 1 from 4.

$$\frac{6^{1}}{\left(-2\right)^{1}}u^{4}v^{3}$$

Divide 6 by -2.

$$-3u^{4}v^{3}$$

Differentiate w.r.t. u

$$-12\left(uv\right)^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{6v^{4}}{-2v}u^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\left(-3v^{3}\right)u^{4})$$

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}.

$$4\left(-3v^{3}\right)u^{4-1}$$

Do the arithmetic.

$$\left(-12v^{3}\right)u^{3}$$