Solve 5^3-{x}^frac{-2{5}}

$${ 5 }^{ 3 } - { x }^{ \frac{ -2 }{ 5 } }$$

Evaluate

$$125-\frac{1}{x^{\frac{2}{5}}}$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$125-x^{\frac{-2}{5}}$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$125-x^{-\frac{2}{5}}$$

Differentiate w.r.t. x

$$\frac{2}{5x^{\frac{7}{5}}}$$

Steps Using Derivative Rule for Sum

Calculate 5 to the power of 3 and get 125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(125-x^{\frac{-2}{5}})$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(125-x^{-\frac{2}{5}})$$

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}.

$$-\frac{2}{5}\left(-1\right)x^{-\frac{2}{5}-1}$$

Multiply -\frac{2}{5} times -1.

$$\frac{2}{5}x^{-\frac{2}{5}-1}$$

Subtract 1 from -\frac{2}{5}.

$$\frac{2}{5}x^{-\frac{7}{5}}$$