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\frac{d}{dx}\left(x^6+\frac{\sin\left(x\right)}{8x^2+1}\right)

Derive the function x^6+(sin(x))/(8x^2+1) with respect to x

Answer

$\frac{\left(1+8x^2\right)\cos\left(x\right)-16x\sin\left(x\right)}{\left(1+8x^2\right)^2}+6x^{5}$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(x^6+\frac{\sin\left(x\right)}{8x^2+1}\right)$
1

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

$\frac{d}{dx}\left(\frac{\sin\left(x\right)}{1+8x^2}\right)+\frac{d}{dx}\left(x^6\right)$

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Answer

$\frac{\left(1+8x^2\right)\cos\left(x\right)-16x\sin\left(x\right)}{\left(1+8x^2\right)^2}+6x^{5}$

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$\frac{d}{dx}\left(x^6+\frac{\sin\left(x\right)}{8x^2+1}\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.29 seconds