Solve yx^2/3x^-2y^4

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

Evaluate

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

Solution Steps

Cancel out y in both numerator and denominator.

$$\frac{x^{2}}{3x^{-2}y^{3}}$$

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

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

Differentiate w.r.t. x

$$\frac{4\times \left(\frac{x}{y}\right)^{3}}{3}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3y^{3}}x^{4})$$

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}.

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

Do the arithmetic.

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