Solve 1+1/(x^2y^4)^1/3

$$\frac { 1 + 1 } { ( x ^ { 2 } y ^ { 4 } ) ^ { 1 / 3 } }$$

Evaluate

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

Solution Steps

Add 1 and 1 to get 2.

$$\frac{2}{\left(x^{2}y^{4}\right)^{\frac{1}{3}}}$$

Expand \left(x^{2}y^{4}\right)^{\frac{1}{3}}.

$$\frac{2}{\left(x^{2}\right)^{\frac{1}{3}}\left(y^{4}\right)^{\frac{1}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$\frac{2}{x^{\frac{2}{3}}\left(y^{4}\right)^{\frac{1}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

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

Differentiate w.r.t. x

$$-\frac{4}{3y^{\frac{4}{3}}x^{\frac{5}{3}}}$$