Solve frac{x^{-2}y^{-2}*9^{-1}*w^{0}}{x^-4*y^-2*q^4*w^3}

$$\frac { x ^ { - 2 } y ^ { - 2 } \cdot 9 ^ { - 1 } \cdot w ^ { 0 } } { x ^ { - 4 } \cdot y ^ { - 2 } \cdot q ^ { 4 } \cdot w ^ { 3 } }$$

Evaluate

$$\frac{x^{2}}{9w^{3}q^{4}}$$

Solution Steps

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

$$\frac{\frac{1}{9}x^{-2}w^{0}}{x^{-4}w^{3}q^{4}}$$

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

$$\frac{\frac{1}{9}w^{0}x^{2}}{w^{3}q^{4}}$$

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

$$\frac{\frac{1}{9}x^{2}}{w^{3}q^{4}}$$

Differentiate w.r.t. x

$$\frac{2x}{9w^{3}q^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{w^{0}}{9y^{2}\times \frac{w^{3}q^{4}}{y^{2}}}x^{-2-\left(-4\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{9w^{3}q^{4}}x^{2})$$

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}.

$$2\times \frac{1}{9w^{3}q^{4}}x^{2-1}$$

Do the arithmetic.

$$\frac{2}{9w^{3}q^{4}}x^{1}$$

For any term t, t^{1}=t.

$$\frac{2}{9w^{3}q^{4}}x$$