Solve {left(x^3right)}^frac{2{9}}

$${ \left( { x }^{ 3 } \right) }^{ \frac{ 2 }{ 9 } }$$

Differentiate w.r.t. x

$$\frac{2}{3\sqrt[3]{x}}$$

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).

$$\frac{2}{9}\left(x^{3}\right)^{\frac{2}{9}-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})$$

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}.

$$\frac{2}{9}\left(x^{3}\right)^{-\frac{7}{9}}\times 3x^{3-1}$$

Simplify.

$$\frac{2}{3}x^{2}\left(x^{3}\right)^{-\frac{7}{9}}$$

Evaluate

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