# Step-by-step Solution

## Find the derivative of $\tan\left(x+1\right)$

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### Videos

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

## Step-by-step solution

Problem to solve:

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

Solving method

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

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

$\sec\left(x+1\right)^2\left(\frac{d}{dx}\left(x\right)+0\right)$

$x+0=x$, where $x$ is any expression

$\sec\left(x+1\right)^2\frac{d}{dx}\left(x\right)$
3

The derivative of the constant function ($1$) is equal to zero

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

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

Any expression multiplied by $1$ is equal to itself

$\sec\left(x+1\right)^2$
4

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

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

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

### Main topic:

Differential Calculus

~ 0.03 s