Techniques of Differentiation - Chain Rule
Techniques of Differentiation - Chain Rule
Find the derivative of each of the following,
- \(y = \left( x + \frac{1}{\sqrt{x}} \right)^{4}\)
- \(y = \left( \frac{x^{4}}{2} + x \right)^{5}\)
- \(\left( \sqrt{x^{5}} - \frac{4}{7x^{2}} \right)^{7}\)
- \(y = (5x^{3} - 4x + 1)^{5}\)
- \(y = \sqrt{5x^{2} + x - 1}\)
- \(y = (x^{4} + 3x^{2} - 1)^{12}\)
- \(y = (1 - 2x + x^{3})^{\tfrac{5}{2}}\)
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Answer:(a) \(4(1-\frac{1}{2x^{3/2}})(x+\frac1{\sqrt{x}})^3\) (b) \(5(2x^3+1)(\frac{x^4}{2}+x)^4\) (c) \(7(\sqrt{x^5}-\frac{4}{7x^2})^6(\frac52\sqrt{x^3}+\frac{8}{7x^3})\) (d) \(5(15x^2-4)(5x^3-4x+1)^4\) (e) \(\frac12(10x+1)(5x^2+x-1)^{-1/2}\) (f) \(24x(2x^2+3)(x^4+3x^2-1)^{11}\) (g) \(\frac52(1-2x+x^3)^{3/2}(3x^2-2)\)
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