Derivative of $g(t) := f(tx + (1 − t)y)-tf(x)-(1-t)f(y)$

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I want to calculate derivative of this function. answer: $$g'(t)=<∇f((tx + (1 − t)y),x-y>-f(x)+f(y)\\ g''(t)=<∇^2f((tx + (1 − t)y)(x-y),x-y>$$ \ I tried but I couldn't.Can you help me please?\

Thank you