Solve 3x^2y^2/2x^-1*4yx^2

$$\frac { 3 x ^ { 2 } y ^ { 2 } } { 2 x ^ { - 1 } \cdot 4 y x ^ { 2 } }$$

Evaluate

$$\frac{3xy}{8}$$

Solution Steps

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

$$\frac{3x^{2}y^{2}}{2x^{1}\times 4y}$$

Cancel out xy in both numerator and denominator.

$$\frac{3xy}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$\frac{3xy}{8}$$

Differentiate w.r.t. x

$$\frac{3y}{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y^{2}}{8yx^{2}}x^{2-\left(-1\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y}{8x^{2}}x^{3})$$

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}.

$$3\times \frac{3y}{8x^{2}}x^{3-1}$$

Do the arithmetic.

$$\frac{9y}{8x^{2}}x^{2}$$