Solve 18x^-5y^4/12x^-3y^-3

$$\frac { 18 x ^ { - 5 } y ^ { 4 } } { 12 x ^ { - 3 } y ^ { - 3 } }$$

Evaluate

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

Solution Steps

Cancel out 6 in both numerator and denominator.

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

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

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

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

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18y^{4}y^{3}}{12}x^{-5-\left(-3\right)})$$

Do the arithmetic.

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

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}.

$$-2\times \frac{3y^{7}}{2}x^{-2-1}$$

Do the arithmetic.

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