Final answer to the problem
$\sec\left(x+1\right)^2$
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Step-by-step Solution
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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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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 ${f'(x) = sec^2(x)\cdot D_x(x)}$
$\frac{d}{dx}\left(x+1\right)\sec\left(x+1\right)^2$
The derivative of the constant function ($1$) is equal to zero
$\frac{d}{dx}\left(x\right)\sec\left(x+1\right)^2$
The derivative of the linear function is equal to $1$
$\sec\left(x+1\right)^2$
2
The derivative of a sum of two or more functions is the sum of the derivatives of each function
$\sec\left(x+1\right)^2$
Final answer to the problem
$\sec\left(x+1\right)^2$
