Solve 6x^10y^4/2x^3y^8

$$\frac { 6 x ^ { 10 } y ^ { 4 } } { 2 x ^ { 3 } y ^ { 8 } }$$

Evaluate

$$\frac{3x^{7}}{y^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{6^{1}x^{10}y^{4}}{2^{1}x^{3}y^{8}}$$

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

$$\frac{6^{1}}{2^{1}}x^{10-3}y^{4-8}$$

Subtract 3 from 10.

$$\frac{6^{1}}{2^{1}}x^{7}y^{4-8}$$

Subtract 8 from 4.

$$\frac{6^{1}}{2^{1}}x^{7}y^{-4}$$

Divide 6 by 2.

$$3x^{7}\times \frac{1}{y^{4}}$$

Differentiate w.r.t. x

$$\frac{21x^{6}}{y^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{4}}{2y^{8}}x^{10-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{y^{4}}x^{7})$$

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}.

$$7\times \frac{3}{y^{4}}x^{7-1}$$

Do the arithmetic.

$$\frac{21}{y^{4}}x^{6}$$