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  • If    then find      <img alt="\frac{d^2 y}{d x^2}"

If   y=secx+e^{x} then find      \frac{d^2 y}{d x^2}.

Option: 1

\sec ^2 x+\tan x


Option: 2

\sec ^3 x+\sec x t a n^2 x


Option: 3

\sec ^3 x+\sec x \tan ^2 x+e^x


Option: 4

\sec ^2 x+\tan x+e^x


Answers (1)

best_answer

Given that y=secx+e^{x}

Differentiate using the trigonometric identities

\begin{aligned} & \frac{d y}{d x}=\left[\sec x \tan x+e^x\right] \\ & \frac{d^2 y}{d x^2}=\left[\sec x \cdot \sec ^2 x+\tan x \cdot \sec x \cdot \tan x\right]+e^x \\ & \frac{d^2 y}{d x^2}=\sec ^3 x+\sec x t a n^2 x+e^x \\ & \end{aligned}

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shivangi.shekhar

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