The function f(r) = tanh(r) is one-to-one and so is invertible. Using our rule/ formula for relating e derivative of an inverse to the derivative of the original function, find the slope of the line tangent to the graph of =5"(x) = arctah(r) when r 0.

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A: We can find the derivative as below

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A: Given function is Differentiating both sides with respect to , we get

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A: Given,          y=5cosx

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Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

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A: Find the derivative of y with respect to the appropriate variable.

Q: I need to find the derivative of the function f(x) = cos-1(ln(sin(3x+1))) but I am unsure how to…

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Q: if the derivative of x2sinx+2xcosx-sinx  is (Ax2+B)(cos(C(x/2))). FInd the value of A, B, and C.

A: Given: x2sinx+2xcosx-sinx Differentiate the equation.…

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Q: Compute the derivative using derivative rules. y= cos(1/x) / (1 +x 2)

A: Derivative: The rate of change of a function with respect to a variable. y=fxy'=limh→∞ f(x+h)-f(x)h

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A: differentiate wrt theta

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A: This question is based on chain rule differentiation.

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A: Given : y = cos-112x

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A: We find the first 4 derivatives using the chain rule

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A: Given:y=arc tancosθFormula:ddxtan-1u=11+u2.dudx

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A: Consider the function  g(x)=tan−1x3

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A: y=cos-1sin-1t

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

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A: Given:

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A: dydx=?

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A: Given functions are sin-1x and cos-1x