Question

y = 2x + 2/x find the derivative f'(x)​

Answer 1

= 2x + 2/x find the derivative f'(x)Step-by-step explanation:

Suppose y=f(z) = well f can be anything. Then we put z=x2−2x+7 and get a new function g(x)=f(x2−2x+7). Some examples:

f(z)=z;f(x2−2x+7)=x2−2x+7=g(x)

f(z)=z2+3;f(x2−2x+7)=(x2−2x+7)2+3=g(x)

f(z)=sin(z);f(x2−2x+7)=sin(x2−2x+7)=g(x)

Now we want to see what we know about the derivative of f(x2−2x+7) when it could take any one of a myriad of forms. We use the chain rule - the derivative of p(q(x)) is q′(x)p′(q(x)) with p=f and q(x)=x2−2x+7 to obtain the derivative

(2x−2)f′(x2−2x+7)

Now we only know f′(10), so we can only deal with

x2−2x+7=10

which reduces to

(x−3)(x+1)=0

So x=3, or x=−1

With x=3 we get 4×2=8.

With x=−1 we get −4×2=−8.

Because the form of f is undefined, we can't say more than this - even that our function is differentiable in other places

Answer 2

Step-by-step explanation:

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