Solve (u^frac{1{3}})^3

$$( u ^ { \frac { 1 } { 3 } } ) ^ { 3 }$$

Evaluate

$$u$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(\sqrt[3]{u}\right)^{3}$$

To raise a power to another power, multiply the exponents.

$$u^{\frac{1}{3}\times 3}$$

Multiply \frac{1}{3} times 3.

$$u$$

Differentiate w.r.t. u

$$1$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$3\left(\sqrt[3]{u}\right)^{3-1}\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt[3]{u})$$

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}.

$$3\left(\sqrt[3]{u}\right)^{2}\times \frac{1}{3}u^{\frac{1}{3}-1}$$

Simplify.

$$u^{-\frac{2}{3}}\left(\sqrt[3]{u}\right)^{2}$$