Solve {left({x}^14+frac{2{}}right)}^frac{2{30}}

$${ \left( { x }^{ 14+ \frac{ 2 }{ } } \right) }^{ \frac{ 2 }{ 30 } }$$

Evaluate

$$x^{\frac{16}{15}}$$

Solution Steps

Anything divided by one gives itself.

$$\left(x^{14+2}\right)^{\frac{2}{30}}$$

Add 14 and 2 to get 16.

$$\left(x^{16}\right)^{\frac{2}{30}}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\left(x^{16}\right)^{\frac{1}{15}}$$

Differentiate w.r.t. x

$$\frac{16\sqrt[15]{x}}{15}$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{14+2}\right)^{\frac{2}{30}})$$

Add 14 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{16}\right)^{\frac{2}{30}})$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{16}\right)^{\frac{1}{15}})$$

To raise a power to another power, multiply the exponents. Multiply 16 and \frac{1}{15} to get \frac{16}{15}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{16}{15}})$$

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

$$\frac{16}{15}x^{\frac{16}{15}-1}$$

Subtract 1 from \frac{16}{15}.

$$\frac{16}{15}\sqrt[15]{x}$$