Solve 9x^3y^5/6x^-6y^-5

$$\frac { 9 x ^ { 3 } y ^ { 5 } } { 6 x ^ { - 6 } y ^ { - 5 } }$$

Evaluate

$$\frac{3x^{9}y^{10}}{2}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{3x^{3}y^{5}}{2x^{-6}y^{-5}}$$

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

$$\frac{3x^{9}y^{10}}{2}$$

Differentiate w.r.t. x

$$\frac{27x^{8}y^{10}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9y^{5}y^{5}}{6}x^{3-\left(-6\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y^{10}}{2}x^{9})$$

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}.

$$9\times \frac{3y^{10}}{2}x^{9-1}$$

Do the arithmetic.

$$\frac{27y^{10}}{2}x^{8}$$