Solve -9x^3y^-2/3x^5y^-4

$$\frac { - 9 x ^ { 3 } y ^ { - 2 } } { 3 x ^ { 5 } y ^ { - 4 } }$$

Evaluate

$$-3\times \left(\frac{y}{x}\right)^{2}$$

Solution Steps

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

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-\frac{9}{y^{2}}\right)y^{4}}{3}x^{3-5})$$

Do the arithmetic.

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

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}.

$$-2\left(-3y^{2}\right)x^{-2-1}$$

Do the arithmetic.

$$6y^{2}x^{-3}$$