Solve {left({x}^frac{4{5}}right)}^5

$${ \left( { x }^{ \frac{ 4 }{ 5 } } \right) }^{ 5 }$$

Differentiate w.r.t. x

$$4x^{3}$$

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).

$$5\left(x^{\frac{4}{5}}\right)^{5-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{4}{5}})$$

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}.

$$5\left(x^{\frac{4}{5}}\right)^{4}\times \frac{4}{5}x^{\frac{4}{5}-1}$$

Simplify.

$$4x^{-\frac{1}{5}}\left(x^{\frac{4}{5}}\right)^{4}$$

Evaluate

$$x^{4}$$