Question

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): 4\(\sqrt x\) -2

Answer 1

Let f(x)= 4\(\sqrt x\)-2
By quotient rule,
f'(x)= \(\frac{d}{dx}\) (4\(\sqrt x\) -2) = \(\frac{d}{dx}\)(4\(\sqrt x\)) - \(\frac{d}{dx}\)(2)
=4 \(\frac{d}{dx}\)(x\(^{\frac{1}{2}}\)) - 0 = 4(\(\frac{1}{2}\)x\(^{\frac{1}{2}-1}\))
=(2x\(^{-\frac{1}{2}}\) ) = \(\frac{1}{\sqrt x}\)