Solve 3xy/y^2*yx^2

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

Evaluate

$$\frac{3}{xy^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Cancel out xy in both numerator and denominator.

$$\frac{3}{xy^{2}}$$

Differentiate w.r.t. x

$$-\frac{3}{\left(xy\right)^{2}}$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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