Solve {left(eta^4right)}^frac{3{2}}

$${ \left( { \eta }^{ 4 } \right) }^{ \frac{ 3 }{ 2 } }$$

Differentiate w.r.t. η

$$6\eta ^{5}$$

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).

$$\frac{3}{2}\left(\eta ^{4}\right)^{\frac{3}{2}-1}\frac{\mathrm{d}}{\mathrm{d}\eta }(\eta ^{4})$$

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}.

$$\frac{3}{2}\sqrt{\eta ^{4}}\times 4\eta ^{4-1}$$

Simplify.

$$6\eta ^{3}\sqrt{\eta ^{4}}$$

Evaluate

$$\eta ^{6}$$