Find the derivative of the following functions

Question:

Find the derivative of the following functions (it is to be understood that abcdp, q, r and s are fixed non-zero constants and m and n are integers): $4 \sqrt{x}-2$

Solution:

Let $f(x)=4 \sqrt{x}-2$

$f^{\prime}(x)=\frac{d}{d x}(4 \sqrt{x}-2)=\frac{d}{d x}(4 \sqrt{x})-\frac{d}{d x}(2)$

$=4 \frac{d}{d x}\left(x^{\frac{1}{2}}\right)-0=4\left(\frac{1}{2} x^{\frac{1}{2}-1}\right)$

$=\left(2 x^{-\frac{1}{2}}\right)=\frac{2}{\sqrt{x}}$

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