Solve 60x^9y^5/4x^6y^4

$$\frac { 60 x ^ { 9 } y ^ { 5 } } { 4 x ^ { 6 } y ^ { 4 } }$$

Evaluate

$$15yx^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{60^{1}x^{9}y^{5}}{4^{1}x^{6}y^{4}}$$

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

$$\frac{60^{1}}{4^{1}}x^{9-6}y^{5-4}$$

Subtract 6 from 9.

$$\frac{60^{1}}{4^{1}}x^{3}y^{5-4}$$

Subtract 4 from 5.

$$\frac{60^{1}}{4^{1}}x^{3}y^{1}$$

Divide 60 by 4.

$$15x^{3}y$$

Differentiate w.r.t. x

$$45yx^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{60y^{5}}{4y^{4}}x^{9-6})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15yx^{3})$$

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}.

$$3\times 15yx^{3-1}$$

Do the arithmetic.

$$45yx^{2}$$