By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh x+4sinh x.

Q: Find y′ if y = tanh−1(sinh x2).

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Q: Find the first and second derivatives.  f(x) = ln(5x+1)  Please explain and show how to do this…

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Q: EX / Show that cosh x-sinhx=1

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Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: = sinh" (tan 3x

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Q: fx ln x dx.

A: According to the guidelines the first question can be solve in multiple question. Kindly repost…

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Given: y=cos4θ

Q: Find the second derivative of the function 2 f(x) = sin (3x). Show your work.

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Q: By using the definition of hyperbolic functions, show that sinh x = 1 (cosh 2x – 1). -

A: Given,         sinh2x=12cosh2x-1

Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: 11. f(x) =log, 1+x

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

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

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Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: dx Tx-1 4

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Q: find derivative y=square root of (1+ x times e^-2x)

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Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) -1 1

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Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

Q: What integrals lead naturally to inverse hyperbolic functions?

A: Assume

Q: Differentiate  f(x)  = log 10  ( 2+ sinx )

A: Rewrite the given function as shown below: fx=log102+sinxfx=ln2+sinxln10        since logab=lnblna

Q: sinh 3x –1 H(x)=: 1+cosh 3x –1

A: Given: H(x)=sinh3x-11+cosh3x-1 To solve: The given function.

Q: Find the indefinite integral and check the result by differentiation. Step 1

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Q: 2. y=cot1-2x 3. y=log22x*

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Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

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Q: Evaluate the integral.

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Q: Find the second-order derivative of the function f(x) = log5 sin x + (2x2 - 8) / (x4 - 4x2). Please…

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Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Using chain rule to compute the derivative for y, consider the solution below.   First of all,…

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: sinh4x cosh 4x dx can best be evaluated by General Power Formula. A True False

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Q: Determine the first derivative of the ff. function y = 400(2)*+3 sin 3x

A: Given: y=4002x+3 sin 3x To Find: First derivative of the given function

Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

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Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

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Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: sinh 2x cosh 3xdx.

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Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: If sinh(x) = 35 =, find the values of the other hyperbolic functions at x. %3D cosh(x) tanh(x)…

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Q: What is the derivative of ln(sec(7x) + tan(7x))?

A: Let y = ln(sec(7x) + tan(7x)).Calculation:Obtain the derivatite of y as follows.

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: 3 sin-xe 5%

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Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below:…

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Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: Use definition of hyperbolic function to prove that 2 sinh x cosh x = sinh 2x. Hence, solve the…

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Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: Solve the first and second derivative of y = cosh2x+ sinhx

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: