Solve (15x^-2y^-2/3xy^-1)

$$( \frac{ 15 { x }^{ -2 } { y }^{ -2 } }{ 3x { y }^{ -1 } } )$$

Evaluate

$$\frac{5}{yx^{3}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{5x^{-2}y^{-2}}{\frac{1}{y}x}$$

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

$$\frac{5}{y^{1}x^{3}}$$

Calculate y to the power of 1 and get y.

$$\frac{5}{yx^{3}}$$

Differentiate w.r.t. x

$$-\frac{15}{yx^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15}{y^{2}\times \frac{3}{y}}x^{-2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{y}x^{-3})$$

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}.

$$-3\times \frac{5}{y}x^{-3-1}$$

Do the arithmetic.

$$\left(-\frac{15}{y}\right)x^{-4}$$