Solve frac{2x^{2}y^2}{4x^2y^4*3x^-3}

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

Evaluate

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

Solution Steps

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

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

Cancel out 2y^{2} in both numerator and denominator.

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

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

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

Multiply 2 and 3 to get 6.

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{2}x^{3}}{12y^{4}}x^{2-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{6y^{2}}x^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{6y^{2}})$$

The derivative of a constant term is 0.

$$0$$