3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the logistic equation: = k(1 – ) y y M Note: The function tanh is the hyperbolic tangent e* - e-* e2x – 1 function: tanh x = ex + e-x e2x + 1

Q: Find the derivative of the function. log4|(3x²-2x) 5/21

A: y=log4⁡|(3x2−2x)5/2|

Q: 1. Logarithmic differentiation. Compute the derivative of each function using logarithmic…

A: Given is the function f(x)=x4(1-2x)x3+2 Take log on both sides of the given function. Then use the…

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A: Step 1: For y=ln(x2+2x+3): Identify the function: y=ln(u), where u=x2+2x+3. Apply the chain rule:…

Q: 3. Use properties of logarithms and/or logarithmic differentiation to find the indicated derivatives…

A: a.)  y =ddxlnx2   ⇒y =2ddxlnx =2x                                                  ln(ab)…

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A:

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A: The Answer is Option A

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A:

Q: 3. Use logarithmic differentiation to find y'; and simplify the result to a "single fraction". x2…

A:

Q: Suppose y is a function of x. Find dy/dx. B only.

A: When there is variable in the base and in the power of a function, we follow the logarithmic…

Q: Find the derivative dv/dpsi of v(x) V()| V(vi) where V(y) = (1 - e-√2 and 16 V (vi) = (1 - e-√2…

A: Given v(ψ)=VψVψi           (1) where Vψ=1-e-16π3ψ2 and Vψi=1-e-16π3ψi2 Since ψi≠ψ and ψi is the…