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Regola di differenziazione della somma Calculator

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1

Here, we show you a step-by-step solved example of règle de la somme de la différenciation. This solution was automatically generated by our smart calculator:

$\frac{d}{dx}\left(4x^3+9x^2-4x-5\right)$

Apply the formula: $\frac{d}{dx}\left(c\right)$$=0$, where $c=-5$

$\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(9x^2\right)+\frac{d}{dx}\left(-4x\right)$
2

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(9x^2\right)+\frac{d}{dx}\left(-4x\right)$

Apply the formula: $\frac{d}{dx}\left(cx\right)$$=c\frac{d}{dx}\left(x\right)$

$4\frac{d}{dx}\left(x^3\right)+\frac{d}{dx}\left(9x^2\right)+\frac{d}{dx}\left(-4x\right)$
3

Apply the formula: $\frac{d}{dx}\left(nx\right)$$=n\frac{d}{dx}\left(x\right)$, where $n=-4$

$\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(9x^2\right)-4\frac{d}{dx}\left(x\right)$
4

Apply the formula: $\frac{d}{dx}\left(x\right)$$=1$

$\frac{d}{dx}\left(4x^3\right)+\frac{d}{dx}\left(9x^2\right)-4$

Apply the formula: $\frac{d}{dx}\left(cx\right)$$=c\frac{d}{dx}\left(x\right)$, where $c=9$ and $x=x^2$

$4\frac{d}{dx}\left(x^3\right)+9\frac{d}{dx}\left(x^2\right)-4$
5

Apply the formula: $\frac{d}{dx}\left(cx\right)$$=c\frac{d}{dx}\left(x\right)$

$4\frac{d}{dx}\left(x^3\right)+9\frac{d}{dx}\left(x^2\right)-4$

Apply the formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}$, where $a=2$

$18x^{\left(2-1\right)}$

Apply the formula: $a+b$$=a+b$, where $a=2$, $b=-1$ and $a+b=2-1$

$18x$
6

Apply the formula: $\frac{d}{dx}\left(x^a\right)$$=ax^{\left(a-1\right)}$, where $a=2$

$4\cdot 3x^{2}+9\cdot 2x-4$
7

Apply the formula: $ab$$=ab$, where $ab=4\cdot 3x^{2}$, $a=4$ and $b=3$

$12x^{2}+9\cdot 2x-4$
8

Apply the formula: $ab$$=ab$, where $ab=9\cdot 2x$, $a=9$ and $b=2$

$12x^{2}+18x-4$

Final answer to the problem

$12x^{2}+18x-4$

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