Solve (x^frac{4{3}})^frac{3{2}}

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

Differentiate w.r.t. x

$$2x$$

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).

$$\frac{3}{2}\left(x^{\frac{4}{3}}\right)^{\frac{3}{2}-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{4}{3}})$$

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}.

$$\frac{3}{2}\sqrt{x^{\frac{4}{3}}}\times \frac{4}{3}x^{\frac{4}{3}-1}$$

Simplify.

$$2\sqrt[3]{x}\sqrt{x^{\frac{4}{3}}}$$

Evaluate

$$x^{2}$$