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Let f(x)=(5x3+3x1)(x1)f\left(x\right)=\left(5x^3+3x-1\right)\left(x-1\right)

ddxf(x)=ddx[(5x3+3x1)(x1)]\frac{d}{dx}f\left(x\right)=\frac{d}{dx}\left[\left(5x^3+3x-1\right)\left(x-1\right)\right]

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f(x)=x327. f\left(x\right)=x^3-27.  

 

 

If f(x) be any real valued function then derivative of f(x) be 

 f (x)=limh0 f(x+h)f(x)h\ f\ '\left(x\right)=\lim _{h\to 0}\ \frac{f\left(x+h\right)-f\left(x\right)}{h}

 

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Hari Iyer
Founder & Chief Nerd @ Kapeesh.io, chat-based 1-on-1 help for students
 f(x)=x5\ f\left(x\right)=|x|-5
To find the limit we need to know what to use for x|x|

limx5 x5\lim _{x\to 5}\ x - 5

=55=0=5-5=0

Since x5x \rightarrow 5, x>0x > 0. This means x=x|x|=x. So use function f(x)=x5f(x) = x - 5 and find the limit by the u... (More)