Solve (x^frac{2{5}})^-2x^frac{7{5}}

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

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{2}{5} and -2 to get -\frac{4}{5}.

$$x^{-\frac{4}{5}}x^{\frac{7}{5}}$$

To multiply powers of the same base, add their exponents. Add -\frac{4}{5} and \frac{7}{5} to get \frac{3}{5}.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply \frac{2}{5} and -2 to get -\frac{4}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-\frac{4}{5}}x^{\frac{7}{5}})$$

To multiply powers of the same base, add their exponents. Add -\frac{4}{5} and \frac{7}{5} to get \frac{3}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{3}{5}})$$

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

$$\frac{3}{5}x^{\frac{3}{5}-1}$$

Subtract 1 from \frac{3}{5}.

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