Solve frac{2x^{2}y^2}{1x^2y^2*3x^-3}

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Differentiate w.r.t. x

$$2x^{2}$$

Solution Steps

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

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

Do the arithmetic.

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

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

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

The derivative of a constant term is 0.

$$0$$