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Rules of Differentiation

Differentiation of Constants and Powers of $x$ worksheet and textbook only Chain Rule Product Rule worksheet and textbook only Quotient Rule worksheet and textbook only
Differentiating Logarithmic Functions
Proof of the derivative of $\ln(x)$ Proof of the derivative of $\log_a x$ Exercises
Differentiating Exponential Functions
Proof of the derivative of $e^x$ Proof of the derivative of $a^x$ Exercises
Differentiating Trigonometric Functions Differentiating Invere Trigonometric Functions Implicit Differentiation

$g\left(x\right)=ax^2+bx+c$ such that $g\left(0\right)=1, g'\left(1\right)=g\left(1\right)$ and $g'\left(-1\right)=g\left(-1\right)$.
Find the values of $a, b$ and $c$.

$a=$