Solve {left({left({x}^frac{-2{3}}right)}^frac{3{5}}right)}^frac{5{4}}

$${ \left( { \left( { x }^{ \frac{ -2 }{ 3 } } \right) }^{ \frac{ 3 }{ 5 } } \right) }^{ \frac{ 5 }{ 4 } }$$

Differentiate w.r.t. x

$$-\frac{sign(x)}{2\left(|x|\right)^{\frac{3}{2}}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply \frac{3}{5} and \frac{5}{4} to get \frac{3}{4}.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{3} and \frac{3}{4} to get -\frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-\frac{1}{2}})$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{1}{2}x^{-\frac{1}{2}-1}$$

Subtract 1 from -\frac{1}{2}.

$$-\frac{1}{2}x^{-\frac{3}{2}}$$

Evaluate

$$\frac{1}{\sqrt{|x|}}$$