Solve 48x^-4y^-1/16x^-13y^-3

$$\frac { 48 x ^ { - 4 } y ^ { - 1 } } { 16 x ^ { - 13 } y ^ { - 3 } }$$

Evaluate

$$3y^{2}x^{9}$$

Solution Steps

Cancel out 16 in both numerator and denominator.

$$\frac{3x^{-4}\times \frac{1}{y}}{x^{-13}y^{-3}}$$

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

$$3y^{2}x^{9}$$

Differentiate w.r.t. x

$$27y^{2}x^{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{48}{y\times \frac{16}{y^{3}}}x^{-4-\left(-13\right)})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$27y^{2}x^{8}$$