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\frac{d}{dx}\left(\cot\left(3x\right)+x\cdot\sin\left(x^3+5\right)\right)

Find the derivative of cot(3x)+xsin(x^3+5)

Answer

$-3\csc\left(3x\right)^2+3x^{3}\cos\left(5+x^3\right)+\sin\left(5+x^3\right)$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(\cot\left(3x\right)+x\cdot\sin\left(x^3+5\right)\right)$
1

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

$\frac{d}{dx}\left(x\sin\left(5+x^3\right)\right)+\frac{d}{dx}\left(\cot\left(3x\right)\right)$

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Answer

$-3\csc\left(3x\right)^2+3x^{3}\cos\left(5+x^3\right)+\sin\left(5+x^3\right)$
$\frac{d}{dx}\left(\cot\left(3x\right)+x\cdot\sin\left(x^3+5\right)\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

0.47 seconds