Key to "Find the derivatives of the following functions with..." - Plainmath

Jason Watson

Answered question

2021-12-03

Find the derivatives of the following functions with respect to x

x = \tan (e^{- y})

Answer & Explanation

Parminquale

Beginner2021-12-04Added 17 answers

Step 1
Given

x = \tan (e^{- y})

Step 2
Differentiating wrt x

e^{- y} = \tan^{- 1} x

Differentiating w.r.t x

e^{- y} (- \frac{d y}{d x}) = \frac{1}{1 + x^{2}}

- e^{- y} \frac{d y}{d x} = \frac{1}{1 + x^{2}}

\frac{d y}{d x} = \frac{- 1}{(1 + x^{2}) e^{- y}}

\frac{d y}{d x} = \frac{- e^{y}}{1 + x^{2}}

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