Additional Exercises in Differentiation

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Differentiate the following functions of [math]x[/math].

Question i \[\left(2x+3\right)^{2}\] Solution
Question ii \[\left(2x+5\right)^{-1}\] Solution
Question iii \[\sqrt[3]{\frac{1}{x}}\] Solution
Question iv \[\sqrt{2x^{3}}\]
Question v \[\frac{1}{3x+2}\]
Question vi \[\frac{1}{\left(2x-1\right)^{\frac{2}{3}}}\]
Question vii \[\left(x^{2}+3\right)^{4}\]
Question viii \[\frac{1}{3x^{2}+2}\]
Question ix \[\sqrt{2x^{3}-3}\]
Question x \[\frac{3}{\sqrt{2+x^{2}}}\]
Question xi \[\frac{1}{1+\sqrt{x}}\]
Question xii \[\frac{1}{\left(1+\sqrt{x}\right)^{2}}\]
Question xiii \[\left(1-\frac{1}{x}\right)^{3}\]
Question xiv \[\left(\frac{x}{2}-\frac{2}{x}\right)^{5}\]
Question xv \[\left(\frac{2}{\sqrt{x}}-1\right)^{-1}\]
Question xvi \[\frac{1}{\left(x^{2}-\sqrt{x}\right)^{2}}\]
Question xvii \[\frac{1}{x+\sqrt{x}}\]
Question xviii \[\sqrt{x-2} \cdot \left(x^{2}+3\right)\]
Question xix \[\frac{x}{\sqrt{1+x^{2}}}\]
Question xx \[\frac{1-x^{2}}{1+x^{2}}\]
Question xxi \[\left(x-1\right)\sqrt{x^{2}+1}\]
Question xxii \[\frac{2x^{2}-x^{3}}{\sqrt{x^{2}-1}}\]
Question xxiii \[\frac{1-\sqrt{x}}{1+\sqrt{x}}\]
Question xxiv \[\sqrt{\frac{1+x}{2+x}}\]