Find the Derivative - d/df f'(x)x^3-12x+3

$f' (x) x^{3} - 12 x + 3$

Step 1

By the Sum Rule, the derivative of $f' (x) x^{3} - 12 x + 3$ with respect to $f$ is $\frac{d}{d f} [f' (x) x^{3}] + \frac{d}{d f} [- 12 x] + \frac{d}{d f} [3]$ .

$\frac{d}{d f} [f' (x) x^{3}] + \frac{d}{d f} [- 12 x] + \frac{d}{d f} [3]$

Step 2

Since $f' (x) x^{3}$ is constant with respect to $f$ , the derivative of $f' (x) x^{3}$ with respect to $f$ is $0$ .

$0 + \frac{d}{d f} [- 12 x] + \frac{d}{d f} [3]$

Step 3

Since $- 12 x$ is constant with respect to $f$ , the derivative of $- 12 x$ with respect to $f$ is $0$ .

$0 + 0 + \frac{d}{d f} [3]$

Step 4

Since $3$ is constant with respect to $f$ , the derivative of $3$ with respect to $f$ is $0$ .

$0 + 0 + 0$

Step 5

Combine terms.

Add $0$ and $0$ .

$0 + 0$

Add $0$ and $0$ .

$0$

Find the Derivative - d/df f'(x)x^3-12x+3

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