How do you find the derivative of $f (x) = [3 {(x)}^{2}] - 4 x$ $f(x) = [3(x)^2] - 4x$ ?

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Answer 1 · 2018-03-31T21:19:04

$f'(x)=6x-4$

We have:

$f(x)=3x^2-4x$

Remember the following rules:

The power rule:
$d/dx[x^n]=nx^(n-1)$ if $n$ is a constant.

The constant multiplication rule:

If a variable is being multiplied by a constant, you can always bring the constant outside the derivative. For example:

$d/dx[3x]=3*d/dx[x]$

Subtraction rule (Here is an example):

$d/dx[x-2x]=d/dx[x]-d/dx[2x]$

Therefore:

$f'(x)=d/dx[3x^2-4x]$

$=>f'(x)=d/dx[3x^2]-d/dx[4x]$

$=>f'(x)=3*d/dx[x^2]-4*d/dx[x^1]$

$=>f'(x)=3*2*x^(2-1)-4*1*x^(1-1)$

$=>f'(x)=6*x^(1)-4*x^(0)$

$=>f'(x)=6*x-4*1$

$=>f'(x)=6x-4$

How do you find the derivative of f(x) = [3(x)^2] - 4xf(x)=[3(x)2]−4xf(x) = [3(x)^2] - 4x?