Solve 6xy^-4/2x^-2y^2

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

Evaluate

$$\frac{3x^{3}}{y^{6}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

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

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

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

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

$$\frac{3x^{3}}{y^{6}}$$

Differentiate w.r.t. x

$$\frac{9x^{2}}{y^{6}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{y^{4}\times 2y^{2}}x^{1-\left(-2\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{y^{6}}x^{3})$$

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}.

$$3\times \frac{3}{y^{6}}x^{3-1}$$

Do the arithmetic.

$$\frac{9}{y^{6}}x^{2}$$