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Sum rule of differentiation Calculator

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1

Solved example of sum rule of differentiation

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

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

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

The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function

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

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$12x^{2}+\frac{d}{dx}\left(9x^2-4x-5\right)$
5

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

$12x^{2}+\frac{d}{dx}\left(9x^2\right)+\frac{d}{dx}\left(-4x-5\right)$
6

The derivative of a function multiplied by a constant ($9$) is equal to the constant times the derivative of the function

$12x^{2}+9\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(-4x-5\right)$
7

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$12x^{2}+18x+\frac{d}{dx}\left(-4x-5\right)$
8

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

$12x^{2}+18x+\frac{d}{dx}\left(-4x\right)+\frac{d}{dx}\left(-5\right)$
9

The derivative of the constant function ($-5$) is equal to zero

$12x^{2}+18x+\frac{d}{dx}\left(-4x\right)$

The derivative of a function multiplied by a constant ($-4$) is equal to the constant times the derivative of the function

$-4\frac{d}{dx}\left(x\right)$

The derivative of the linear function is equal to $1$

$-4$
10

The derivative of the linear function times a constant, is equal to the constant

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

Final Answer

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

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