Solve -4x^14y^6/2x^4y^3

$$\frac { - 4 x ^ { 14 } y ^ { 6 } } { 2 x ^ { 4 } y ^ { 3 } }$$

Evaluate

$$-2y^{3}x^{10}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-4\right)^{1}x^{14}y^{6}}{2^{1}x^{4}y^{3}}$$

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

$$\frac{\left(-4\right)^{1}}{2^{1}}x^{14-4}y^{6-3}$$

Subtract 4 from 14.

$$\frac{\left(-4\right)^{1}}{2^{1}}x^{10}y^{6-3}$$

Subtract 3 from 6.

$$\frac{\left(-4\right)^{1}}{2^{1}}x^{10}y^{3}$$

Divide -4 by 2.

$$-2x^{10}y^{3}$$

Differentiate w.r.t. x

$$-20y^{3}x^{9}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{4y^{6}}{2y^{3}}\right)x^{14-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-2y^{3}\right)x^{10})$$

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}.

$$10\left(-2y^{3}\right)x^{10-1}$$

Do the arithmetic.

$$\left(-20y^{3}\right)x^{9}$$