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