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

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

Evaluate

$$\frac{2y^{13}}{x^{7}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -4 and -4 to get 16.

$$\frac{y^{16}\times 2yx^{-4}}{x^{3}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 16 and 1 to get 17.

$$\frac{y^{17}\times 2x^{-4}}{x^{3}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{2x^{-4}y^{13}}{x^{3}}$$

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

$$\frac{2y^{13}}{x^{7}}$$

Differentiate w.r.t. x

$$-\frac{14y^{13}}{x^{8}}$$