Solve 5+{left({x}^frac{2{15}}right)}^frac{11{4}}

$$5+ { \left( { x }^{ \frac{ 2 }{ 15 } } \right) }^{ \frac{ 11 }{ 4 } }$$

Differentiate w.r.t. x

$$\frac{11sign(x)}{30\left(|x|\right)^{\frac{19}{30}}}$$

Steps Using Derivative Rule for Sum

To raise a power to another power, multiply the exponents. Multiply \frac{2}{15} and \frac{11}{4} to get \frac{11}{30}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5+x^{\frac{11}{30}})$$

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}.

$$\frac{11}{30}x^{\frac{11}{30}-1}$$

Subtract 1 from \frac{11}{30}.

$$\frac{11}{30}x^{-\frac{19}{30}}$$

Evaluate

$$\left(|x|\right)^{\frac{11}{30}}+5$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{2}{15} and \frac{11}{4} to get \frac{11}{30}.

$$5+x^{\frac{11}{30}}$$