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Step-by-step Solution

Find the derivative of tan(x+1)

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Answer

$\sec\left(x+1\right)^2$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\tan\left(x+1\right)\right)$
1

The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if ${f(x) = tan(x)}$, then ${f'(x) = sec^2(x)\cdot D_x(x)}$

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

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

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

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Answer

$\sec\left(x+1\right)^2$

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$\frac{d}{dx}\left(\tan\left(x+1\right)\right)$

Main topic:

Differential calculus

Used formulas:

3. See formulas

Time to solve it:

~ 0.33 seconds