Solve frac{(m^2n^frac{1{2}})^0}{n^frac{3{4}}}

$$\frac { ( m ^ { 2 } n ^ { \frac { 1 } { 2 } } ) ^ { 0 } } { n ^ { \frac { 3 } { 4 } } }$$

Differentiate w.r.t. n

$$-\frac{3}{4n^{\frac{7}{4}}}$$

Steps Using Chain Rule

Calculate m^{2}n^{\frac{1}{2}} to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n^{\frac{3}{4}}})$$

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).

$$-\left(n^{\frac{3}{4}}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}n}(n^{\frac{3}{4}})$$

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}.

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

Simplify.

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

Evaluate

$$\frac{1}{n^{\frac{3}{4}}}$$