Solve (x^4)^9/2

$$( x ^ { 4 } ) ^ { 9 / 2 }$$

Differentiate w.r.t. x

$$18x^{17}$$

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).

$$\frac{9}{2}\left(x^{4}\right)^{\frac{9}{2}-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{4})$$

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}.

$$\frac{9}{2}\left(x^{4}\right)^{\frac{7}{2}}\times 4x^{4-1}$$

Simplify.

$$18x^{3}\left(x^{4}\right)^{\frac{7}{2}}$$

Evaluate

$$x^{18}$$