Answered: "Solve the derivatives. z=ecos⁡(2x)" - Plainmath

allhvasstH

Answered question

2021-09-20

Solve the derivatives.

z = e^{\cos (2 x)}

Answer & Explanation

hosentak

Skilled2021-09-21Added 100 answers

Step 1
Given:

z = e^{\cos (2 x)}

Derivation on both sides

\frac{d z}{d x} = \frac{d}{d x} (e^{\cos (2 x)})

Applying exponential power rule

{[e^{u (x)}]}^{'} = e^{u (x)} \cdot u^{'} (x)

Step 2

= e^{\cos (2 x)} \cdot \frac{d}{d x} [\cos (2 x)]

= e^{\cos (2 x)} (- \sin (2 x)) \cdot \frac{d}{d x} [2 x]

= - e^{\cos (2 x)} \cdot 2 \cdot \frac{d}{d x} [x] \cdot \sin (2 x)

= - e^{\cos (2 x)} \cdot 2 \cdot 1 \cdot \sin (2 x)

Therefore

\frac{d z}{d x} = - 2 e^{\cos (2 x)} \sin (2 x)

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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