Solve 6x^2y^2/3x^-6y^4

$$\frac { 6 x ^ { 2 } y ^ { 2 } } { 3 x ^ { - 6 } y ^ { 4 } }$$

Evaluate

$$\frac{2x^{8}}{y^{2}}$$

Solution Steps

Cancel out 3y^{2} in both numerator and denominator.

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

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

$$\frac{2x^{8}}{y^{2}}$$

Differentiate w.r.t. x

$$\frac{16x^{7}}{y^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{2}}{3y^{4}}x^{2-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{y^{2}}x^{8})$$

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}.

$$8\times \frac{2}{y^{2}}x^{8-1}$$

Do the arithmetic.

$$\frac{16}{y^{2}}x^{7}$$