Solve operatorname{de}(x^2)(x^1/3)(x^-3)

$$\operatorname { de } ( x ^ { 2 } ) ( x ^ { 1 / 3 } ) ( x ^ { - 3 } )$$

Evaluate

$$\frac{ed}{x^{\frac{2}{3}}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{3} to get \frac{7}{3}.

$$dex^{\frac{7}{3}}x^{-3}$$

To multiply powers of the same base, add their exponents. Add \frac{7}{3} and -3 to get -\frac{2}{3}.

$$dex^{-\frac{2}{3}}$$

Differentiate w.r.t. x

$$-\frac{2ed}{3x^{\frac{5}{3}}}$$