Understanding Differential Calculus: Solving Homework Equations

s883
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Homework Statement


Could anyone explain me how to solve this?

Homework Equations



f(x) =
1/x2 + 4x + 9 + x4 , f’”’(-2) =


The Attempt at a Solution

 
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Hello s883! :smile: It means to take the 4th derivative of the given function f(x) and then evaluate the resulting expression at x = -2. And I would probably put calculus questions in the calculus forum for next time :wink:
 
I assume you mean f(x) = 1/x^2 + 4x + 9 + x^4= x^{-2}+ 4x+ 9+ x^4.

Can you find f'(x) using the "power rule" ((x^n)'= n x^{n-1})?

What about f'' and f'''?

Now do f''''.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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