Solve {left(x^91right)}^frac{2{30}}

$${ \left( { x }^{ 91 } \right) }^{ \frac{ 2 }{ 30 } }$$

Evaluate

$$x^{\frac{91}{15}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\sqrt[15]{x^{91}}$$

To raise a power to another power, multiply the exponents.

$$x^{91\times \frac{1}{15}}$$

Multiply 91 times \frac{1}{15}.

$$x^{\frac{91}{15}}$$

Differentiate w.r.t. x

$$\frac{91x^{\frac{76}{15}}}{15}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$\frac{1}{15}\left(x^{91}\right)^{\frac{1}{15}-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{91})$$

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}.

$$\frac{1}{15}\left(x^{91}\right)^{-\frac{14}{15}}\times 91x^{91-1}$$

Simplify.

$$\frac{91}{15}x^{90}\left(x^{91}\right)^{-\frac{14}{15}}$$