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The derivative of the function f(x)=−3x2+6x−4f(x)=-3x^2+6x-4f(x)=−3x2+6x−4​ is given by:
Question

The derivative of the function f(x)=3x2+6x4f(x)=-3x^2+6x-4​ is given by:

A.

6x+66x+6​​

B.

6x66x-6​​

C.

6x6-6x-6​​

D.

6x+6-6x+6​​

Correct option is D

Differentiate term by term:f(x)=ddx(3x2)+ddx(6x)+ddx(4)f(x)=32x1+610f(x)=6x+6\begin{aligned}&\text{Differentiate term by term:} \\&f'(x) = \frac{d}{dx}(-3x^2) + \frac{d}{dx}(6x) + \frac{d}{dx}(-4) \\&f'(x) = -3 \cdot 2x^1 + 6 \cdot 1 - 0 \\&f'(x) = -6x + 6\end{aligned}​​

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