Solve 9x^3y^0/7x^5y^2

$$\frac { 9 x ^ { 3 } y ^ { 0 } } { 7 x ^ { 5 } y ^ { 2 } }$$

Evaluate

$$\frac{9}{7\left(xy\right)^{2}}$$

Solution Steps

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

$$\frac{9y^{0}}{7x^{2}y^{2}}$$

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

$$\frac{9}{7x^{2}y^{2}}$$

Differentiate w.r.t. x

$$-\frac{18}{7y^{2}x^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9y^{0}}{7y^{2}}x^{3-5})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{7y^{2}}x^{-2})$$

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}.

$$-2\times \frac{9}{7y^{2}}x^{-2-1}$$

Do the arithmetic.

$$\left(-\frac{18}{7y^{2}}\right)x^{-3}$$