Find the derivative of each of the following functions with respect to $x$. \(f(x) = \frac{(x+3)^2

Question

Find the derivative of each of the following functions with respect to $x$. $f(x) = \frac{(x+3)^2}{x^2+5x+6}$ $f(x) = \frac{4x^2+4x+1}{(2x+1)^{\frac{1}{2}}}$ $f(x) = \frac{3e+2}{1+2x+4x^2}$ $f(x) = \sqrt{\frac{\pi(x^2-1)}{x-1}}$

Accepted Answer

(i) $-\dfrac1{(x+2)^2}$ (ii) $3\sqrt{2x+1}$ (iii) $-\dfrac{(3e+2)(8x+2)}{(4x^2+2x+1)^2}$ (iv) $\dfrac{\sqrt{\pi}}{2\sqrt{x+1}}$

Techniques of Differentiation - Quotient Rule

Techniques of Differentiation - Quotient Rule

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