🎁BACK-TO-SCHOOL DEAL. Subscribe Now to get 40% OFF at only 8.49 USD/month, only valid until Sep 30th, 2024

Question

Question
If $y=e^{\sqrt{x}}+e^{-\sqrt{x}}$ then $\frac{d y}{d x}$ equals (A) $\frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 \sqrt{x}}$ (B) $\frac{e^{\sqrt{x}}-e^{-\sqrt{x}}}{2 x}$ (C) $\frac{1}{2 \sqrt{x}} \sqrt{y^{2}-4}$ (D) $\frac{1}{2 \sqrt{x}} \sqrt{y^{2}+4}$

Asked By CosmicGlider20 at

Answered By Expert

Felix

Expert · 4.3k answers · 4k people helped

Sign in to see the answer

Solution By Steps

Step 1: Differentiate each term

To find

\frac{d y}{d x}, we need to differentiate

y = e^{\sqrt{x}} + e^{-\sqrt{x}} with respect to

x.

Step 2: Apply the chain rule

For

e^{\sqrt{x}}, let

u = \sqrt{x}, then

\frac{d}{dx} e^{\sqrt{x}} = e^{\sqrt{x}} \cdot \frac{d}{dx} \sqrt{x} = e^{\sqrt{x}} \cdot \frac{1}{2\sqrt{x}}.

For

e^{-\sqrt{x}}, let

u = -\sqrt{x}, then

\frac{d}{dx} e^{-\sqrt{x}} = e^{-\sqrt{x}} \cdot \frac{d}{dx} (-\sqrt{x}) = e^{-\sqrt{x}} \cdot \left(-\frac{1}{2\sqrt{x}}\right).

Step 3: Combine the results

Combining the derivatives, we get:

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

Final Answer

The derivative of

y = e^{\sqrt{x}} + e^{-\sqrt{x}} with respect to

x is:

\boxed{A}

🧑‍🏫 More Questions

Phil "Tiger Woods of Poker" Ivey (Superstars of Poker; Texas Hold'Em) compare it with the Wager by David Grann

In silent rooms, where sorrows rest, A lonely heart, by grief oppressed. The haunting notes, a somber tune, As shadows dance beneath the moon. A bittersweet embrace, it brings, The anguished whispers music sings. Chatbote2 The power of music can be strong. It can make us feel we don't fit in. It can bring us joy or make us weep. It can make us laugh or makts us sleep. it can fill our hearts with love and pain. And make us feel we're not the same. Charbot $\pi 1$ is a better responae Gatbot 8 2 is a better response Pease explain your answer in 2-3+ sersences. (The more insighctul and wel-reasoned explanation you write, the bettec, since we prioritise high-qualty writing.)

Which is the best definition of a triangle? A. A figure formed by four segments connecting four noncollinear points B. A figure formed by three segments connecting three noncollinear points C. A figure formed by four collinear points D. A figure formed by three parallel segments SUBMIT

Trusted Workforce 2.0 is an initiative to modernize federal personnel vetting. The reforms focus on: Continuous Vetting Risk Management Increased workforce mobility A culture of trust All of the above

4. The district manager sees that sales figures have declined at a store for three straight months. She decides to replace the store manager. Which of these best describes the error in the district manager's thinking? 1 Marks A. Fundamental bias B. Self-serving bias C. Attributional bias D. Assumption error