Solve 5x^5y^4/35xy^2

$$\frac { 5 x ^ { 5 } y ^ { 4 } } { 35 x y ^ { 2 } }$$

Evaluate

$$\frac{y^{2}x^{4}}{7}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{5^{1}x^{5}y^{4}}{35^{1}x^{1}y^{2}}$$

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

$$\frac{5^{1}}{35^{1}}x^{5-1}y^{4-2}$$

Subtract 1 from 5.

$$\frac{5^{1}}{35^{1}}x^{4}y^{4-2}$$

Subtract 2 from 4.

$$\frac{5^{1}}{35^{1}}x^{4}y^{2}$$

Reduce the fraction \frac{5}{35} to lowest terms by extracting and canceling out 5.

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

Differentiate w.r.t. x

$$\frac{4y^{2}x^{3}}{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{4}}{35y^{2}}x^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{2}}{7}x^{4})$$

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}.

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

Do the arithmetic.

$$\frac{4y^{2}}{7}x^{3}$$