Solve x^2/4x^3y^4

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

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4y^{4}}x^{2-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4y^{4}}\times \frac{1}{x})$$

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}.

$$-\frac{1}{4y^{4}}x^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{1}{4y^{4}}\right)x^{-2}$$

Evaluate

$$\frac{1}{4xy^{4}}$$

Solution Steps

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

$$\frac{1}{4xy^{4}}$$