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### Section 3.12 : Higher Order Derivatives

For problems 1 – 5 determine the fourth derivative of the given function.

1. $$h\left( t \right) = 3{t^7} - 6{t^4} + 8{t^3} - 12t + 18$$ Solution
2. $$V\left( x \right) = {x^3} - {x^2} + x - 1$$ Solution
3. $$\displaystyle f\left( x \right) = 4\,\sqrt{{{x^3}}} - \frac{1}{{8{x^2}}} - \sqrt x$$ Solution
4. $$\displaystyle f\left( w \right) = 7\sin \left( \frac{w}{3} \right) + \cos \left( {1 - 2w} \right)$$ Solution
5. $$y = {{\bf{e}}^{ - 5z}} + 8\ln \left( {2{z^4}} \right)$$ Solution

For problems 6 – 9 determine the second derivative of the given function.

1. $$g\left( x \right) = \sin \left( {2{x^3} - 9x} \right)$$ Solution
2. $$z = \ln \left( {7 - {x^3}} \right)$$ Solution
3. $$\displaystyle Q\left( v \right) = \frac{2}{{{{\left( {6 + 2v - {v^2}} \right)}^4}}}$$ Solution
4. $$H\left( t \right) = {\cos ^2}\left( {7t} \right)$$ Solution

For problems 10 & 11 determine the second derivative of the given function.

1. $$2{x^3} + {y^2} = 1 - 4y$$ Solution
2. $$6y - x{y^2} = 1$$ Solution