Question 199632
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For a) use *[tex \Large f(x) = x^n \ \ \Rightarrow\ \ f'(x) = nx^{n-1}] and the fact that the derivative of the sum is the sum of the derivatives.


For b) do the same thing, but realize that *[tex \Large \sqrt{x^4} = \left(\sqrt{x}\right)^4 = x^2]


For c) remember that *[tex \Large (a^n)^m = a^{nm}] and then use the same process as for a)


For d) use the quotient rule:


If *[tex \Large f(x) = \frac{g(x)}{h(x)}] where both *[tex \Large g(x)] and *[tex \Large h(x)] are differentiable and *[tex \Large h(x) \neq 0] then *[tex \Large f'(x) = \frac{g'(x)h(x)-g(x)h'(x)}{\left(h(x)\right)^2]


For e) use the chain rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}]


But you will need to apply it twice working from the inside out.


For f) use the product rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)=g(x)h(x) \ \ \Rightarrow\ \ f'(x) = g'(x)h(x)+g(x)h'(x)]


If you want me to actually do these for you, write back and we'll talk.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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