Higher Order Derivatives and Their Notations

$$g\ '\left(k\right)$$

$$\frac{dk}{du}$$

$$\frac{du}{dk}$$

$$\frac{d}{du}\left[g\left(k\right)\right]$$

$$\frac{d}{dk}\left[g\left(k\right)\right]$$

$$u\ '''''$$

$$\frac{d^5u}{dk^5}$$

$$\frac{du^5}{d^5k}$$

$$g^{\left(5\right)}\left(x\right)$$

$$\frac{d^{'''''}u}{dk'''''}$$

$$192$$

$$32x^3$$

$$192x$$

$$8x^4$$

$$\cos x$$

$$\sin x$$

$$-\ \sin x$$

$$-\ \cos\ x$$

$$\sin\theta$$

$$\cos\theta$$

$$-\ \sin\theta$$

$$-\ \cos\theta$$

$$18m^{\frac{4}{3}}$$

$$\frac{8}{\sqrt[3]{m^2}}$$

$$18\sqrt[3]{m^4}$$

$$8m^{-\frac{2}{3}}$$

$$-\ \sin\theta$$

$$\cos\theta$$

$$\sin\theta$$

$$-\ \cos\theta$$

$$24x^2$$

$$48x$$

$$48$$

$$0$$

Cannot be determined

$$\sin\theta$$

$$\cos\theta$$

$$-\ \sin\theta$$

$$-\ \cos\theta$$

Cannot be determined

$$\sin\theta$$

$$\cos\theta$$

$$-\ \sin\theta$$

$$-\ \cos\theta$$

Cannot be determined