$\frac{\mathrm{d}}{\mathrm{d}x}\left( {{x}^{n}} \right)=n{{x}^{n-1}}$, where $n$ is a constant.

Question

$\frac{\mathrm{d}}{\mathrm{d}x}\left( {{x}^{n}} \right)=n{{x}^{n-1}}$, where $n$ is a constant. Find the derivative of each of the following, $y={{x}^{6}}$ $y=\frac{1}{{{x}^{5}}}$ $y=\sqrt{x}$ $y=1$

Accepted Answer

(a) $6x^5$. (b) $-\frac5{x^6}$, $x\ne0$. (c) $\frac1{2\sqrt x}$, $x>0$. (d) $0$.

Derivative of Power Functions

Derivative of Power Functions

Solution:

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