Solve 14x^3y^5/2xy^2

$$\frac { 14 x ^ { 3 } y ^ { 5 } } { 2 x y ^ { 2 } }$$

Evaluate

$$7x^{2}y^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{14^{1}x^{3}y^{5}}{2^{1}x^{1}y^{2}}$$

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

$$\frac{14^{1}}{2^{1}}x^{3-1}y^{5-2}$$

Subtract 1 from 3.

$$\frac{14^{1}}{2^{1}}x^{2}y^{5-2}$$

Subtract 2 from 5.

$$\frac{14^{1}}{2^{1}}x^{2}y^{3}$$

Divide 14 by 2.

$$7x^{2}y^{3}$$

Differentiate w.r.t. x

$$14xy^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14y^{5}}{2y^{2}}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7y^{3}x^{2})$$

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}.

$$2\times 7y^{3}x^{2-1}$$

Do the arithmetic.

$$14y^{3}x^{1}$$

For any term t, t^{1}=t.

$$14y^{3}x$$