Prove the differentiation formula. d dx Let y = sech(x), then, in exponential terms, y = 11 Taking the derivative, in exponential terms, gives the following. dy dx = -[sech(x)] = -sech(x) tanh(x) et X -2 = -sech(x) tanh(x) + e-x et ] ----) -e-x ex + ex

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A: We have to find out the first derivative  .

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A: The solution are next step

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A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

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A: Given, function is

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A:

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: xy = e2x; y 2х ху — е

A: We will find y' as following.

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A: To find the derivative of the below expression. fy=9tany−y2−12y3y

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A: given: f(x)=3-xex

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A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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Q: Instruction: please show complete and detail solutions. Expand the power of the binomial: (i)…

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Q: Evaluate the derivatives. Do not simplify. (a) ey - y² = ln x tanz (b) y = (secx)*

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Q: Use the product rule to find the derivative. y = (2x²+5)(3x - 2)

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A: Given that From this graph we see that there is a local maximum at some point.  It means f"(c)=0…

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Q: Find the derivative of the function. y' = y = 6-3x Need Help? Read It Watch It

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Q: Calculate the derivative of the function. 1 h(x) = (3.1x - 4)2 (3.1x – 4)2 = (x),4 Need Help? Read…

A: It is required to find the derivative of the given function h(x)

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A: g(x)=(ln x)13 We need to find g'(x)

Q: and the 1st derivative of x³ + y³ - 6xy = 0

A: Topic: - application of derivatives