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

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

Evaluate

$$\frac{1}{6yx^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{2x^{3}y^{3}}{4x^{6}y^{4}\times 3}$$

Cancel out 2x^{3}y^{3} in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{1}{6yx^{3}}$$

Differentiate w.r.t. x

$$-\frac{1}{2yx^{4}}$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6yx^{3}}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{6yx^{3}})$$

The derivative of a constant term is 0.

$$0$$