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Alenkinab [10]
2 years ago
13

Math- Differentiation . Could you help me to solve this question?

Mathematics
1 answer:
Arlecino [84]2 years ago
4 0

Answer:

Step-by-step explanation:

Hello, first of all we can find a value for f(1)

xf(x)+f(x^2)=2 \\\\\text{So for x = 1, it gives}\\\\f(1)+f(1^2)=f(1)+f(1)=2f(1)=2\\\\ f(1) =1

And we can get the derivative of the equation so.

(uv)'=u'v+uv' \text{ and } \dfrac{df(x^2)}{dx}=2xf'(x^2) \text{ so we can write}\\\\f(x)+xf'(x)+2xf'(x^2)=0\\\\\text{And then, for x = 1}\\\\f(1)+f'(1)+2f'(1)=0\\\\ f(1)+3f'(1)=0\\\\ 3f'(1)=-f(1)=-1\\\\\large \boxed{ f'(1)=-\dfrac{1}{3} }

Thank you

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