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Sum rule of differentiation Calculator

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1

Solved example of basic derivatives

$\frac{d}{dx}\left(4\cos\left(3x\right)-3\sin\left(4x\right)\right)$
2

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

$\frac{d}{dx}\left(4\cos\left(3x\right)\right)+\frac{d}{dx}\left(-3\sin\left(4x\right)\right)$
3

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$4\frac{d}{dx}\left(\cos\left(3x\right)\right)+\frac{d}{dx}\left(-3\sin\left(4x\right)\right)$
4

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$4\frac{d}{dx}\left(\cos\left(3x\right)\right)-3\frac{d}{dx}\left(\sin\left(4x\right)\right)$
5

The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$

$4\frac{d}{dx}\left(\cos\left(3x\right)\right)-3\cos\left(4x\right)\frac{d}{dx}\left(4x\right)$

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$-12\cos\left(4x\right)\frac{d}{dx}\left(x\right)$

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

$-12\cos\left(4x\right)$
6

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

$4\frac{d}{dx}\left(\cos\left(3x\right)\right)-12\cos\left(4x\right)$
7

The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if $f(x) = \cos(x)$, then $f'(x) = -\sin(x)\cdot D_x(x)$

$-4\sin\left(3x\right)\frac{d}{dx}\left(3x\right)-12\cos\left(4x\right)$

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$-12\sin\left(3x\right)\frac{d}{dx}\left(x\right)$

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

$-12\sin\left(3x\right)$
8

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

$-12\sin\left(3x\right)-12\cos\left(4x\right)$

Answer

$-12\sin\left(3x\right)-12\cos\left(4x\right)$

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