Question: Find the derivative for given functions

Hi Max,

I know you are the smartest cookie in the world.

Everyone here knows it too.

So please do not do all of anyone's homework.

How much do you think someone learns when you do all their homework for them ?

Also,

When you post an answer can you be sure to include some ordinary type in it somewhere.

If it only has LaTex then other people cannot hyperlink into it from the answer page.

I usually get around this by copying the original question in first.

If the question is all latex then I would make up some thing to put first.  :)

I am not referring to this answer, I am just talking about answers in general :)

Thanks :)

anyone can help me

$1.\\ f(x) = 5\pi^2\\ f'(x) = 0\text{ as it is a constant}\\ ......................................................\\ 2.\\ f(x) = 5\sqrt x\\ f'(x) = \dfrac{5}{2\sqrt x}\\......................................................\\ 3.\\ f(x) = \dfrac{1}{x^4}=x^{-4}\\ f'(x) = -4x^{-5}=-\dfrac{4}{x^5}\\......................................................\\ 4.\\ f(x) = 2x^7 - 5x^{-7}\\ f'(x) = 14x^6 +35x^{-6}=14x^6 + \dfrac{35}{x^6}\\......................................................\\ 5.\\ f(x) = \dfrac{2x-1}{x^3}=\left(x^{-3}\right)(2x-1)=2x^{-2}-x^{-3}\\ f'(x) = -4x^{-3} +3x^{-4}=-\dfrac{4}{x^3}+\dfrac{3}{x^4}\\ f'(1) = -\dfrac{4}{1^3}+\dfrac{3}{1^4}=-4 + 3 = -1 \\\text{P.S.: Need not use quotient rule nor product rule}\\ ......................................................\\ 6.\\ f(x) = 3x^4 \ln x\\ f'(x) = (12x^3)(\ln x)+(3x^4)(\dfrac{1}{x})=12x^3\ln x + 3x^3\\ f'(1) = 12(1^3)\ln 1 + 3(1^3)=12(0) + 3(1) = 3 \\......................................................\\ 7.\\ f(x)=8\sqrt x + 6x^{3/4}=8x^{1/2}+6x^{3/4}\\ f'(x) = \dfrac{4}{\sqrt x}+\dfrac{9}{2x^{1/4}}\\......................................................\\8.\\ y=\dfrac{5}{x^2}-\dfrac{3}{\sqrt x}+5x^4 = 5x^{-2} - 3x^{-1/2} + 5x^4\\ \dfrac{dy}{dx} = -10x^{-3} +\dfrac{3}{2x^{3/2}}+20x^3 = -\dfrac{10}{x^3}+\dfrac{3}{2x^{3/2}}+20x^3\\​......................................................\\ 9.\\ y = (6x^3 + 2)(5x - 3)\\ \dfrac{dy}{dx} = (18x^2)(5x - 3) + (6x^3 + 2)(5) = 120 x^3 -54x^2+10\\​......................................................\\ 10.\\ f(t) = \dfrac{(8t-3)(2t+5)}{t-7}= \dfrac{16t^2 +34t-15}{t-7} = 16t + 146 +\dfrac{1007}{t-7}\\ f'(t) = 16 - 1007(t-7)^{-2}=16-\dfrac{1007}{(t-7)^2}\\ f'(1) = 16 - \dfrac{1007}{(1-7)^2}=16 - 27\dfrac{35}{36} = -\dfrac{431}{36}$