Solve 33x^5y^-4/11x^3y^2

$$\frac { 33 x ^ { 5 } y ^ { - 4 } } { 11 x ^ { 3 } y ^ { 2 } }$$

Evaluate

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

Solution Steps

Cancel out 11x^{3} in both numerator and denominator.

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33}{y^{4}\times 11y^{2}}x^{5-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{y^{6}}x^{2})$$

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}.

$$2\times \frac{3}{y^{6}}x^{2-1}$$

Do the arithmetic.

$$\frac{6}{y^{6}}x^{1}$$

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

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