Solve (n^frac{1{4}})^2

$$( n ^ { \frac { 1 } { 4 } } ) ^ { 2 }$$

Differentiate w.r.t. n

$$\frac{1}{2\sqrt{n}}$$

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).

$$2\left(\sqrt[4]{n}\right)^{2-1}\frac{\mathrm{d}}{\mathrm{d}n}(\sqrt[4]{n})$$

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}.

$$2\left(\sqrt[4]{n}\right)^{1}\times \frac{1}{4}n^{\frac{1}{4}-1}$$

Simplify.

$$\frac{1}{2}n^{-\frac{3}{4}}\left(\sqrt[4]{n}\right)^{1}$$

For any term t, t^{1}=t.

$$\frac{1}{2}n^{-\frac{3}{4}}\sqrt[4]{n}$$

Evaluate

$$\sqrt{n}$$