f ^ { \prime } ( x ) = 3 x ^ { 2 } d x
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for f
f\in \mathrm{R}
d=0\text{ or }x=0
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\frac{\mathrm{d}}{\mathrm{d}x}(f)x=3x^{3}d
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
3x^{3}d=\frac{\mathrm{d}}{\mathrm{d}x}(f)x
Swap sides so that all variable terms are on the left hand side.
3x^{3}d=0
The equation is in standard form.
d=0
Divide 0 by 3x^{3}.
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