Find the derivative of the following functions. (a) f(x) = tan(x) tanh(x) (b) g(x) = e** cosh(2æ) coth x (c) h(x) x + sech(x?)

Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: 4. Find the derivative of the function f(x) = (sin x)c0s ". COS x

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Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1 + ln t/1 - ln t

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Q: Find a function with derivative equal to g(x) = cos(x)e³sin(x)

A: To find a function with derivative equal to gx=cosx e5 sinx

Q: Find the derivative of the function. y = tan an-¹ (√x-4)

A: We can find the derivative using chain rule as below.

Q: Find the derivative of y = (tan x)cos: COs x .

A: Given : y=(tanx)cosx

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: Find the derivative of the function. g(x) = arccos(x) / x+7   g'(x)=__________________

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Q: Find the derivative of the function. x coS X y = e*cos x

A: Differentiation is the rate of change of some variable with respect to the other variable. Chain…

Q: Find the derivative of function and simply it whenever possible y= ln(ln sec x)

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 x - x sech-1 x

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (sec θ + tan θ)

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

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 (1/2)θ

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Q: y = In- e 2x+1

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Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: Find the derivative of the function g(x)= tanx/e^x.

A: This problem can be solved by the quotient rule in derivatives.

Q: 2) Let y = xe* and find the first derivative y'. Where is y'>0?What does this tell you about the…

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Q: find the derivative of y with respect to the appropriatevariable. y = √(s2 - 1) - sec-1 s

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Q: 2) Find nth derivative of the following function f(x) = ex

A: Given query is to find the nth derivative of the expression.

Q: y = x*(1 – In x4)

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Q: 8. Find the derivative of the function. y= In(1+x)

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Q: 2. Use implicit differentiation to find the derivative of y with respect to x for the following: xe…

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Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (1/x)

A: To find dydx, rewrite the equation and then differentiate with respect to x.…

Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

Q: find the derivative of y with respect to the appropriatevariable. y = ln (tan-1 x)

A: The given function is y=lntan-1x

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

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Q: Find the derivative of the function .

A: Given a function f(x)=2x3+3 cos x f(x)=2(x)1/3+3 cos x      =2x-1/3+3 cos x We, use the following…

Q: Find the derivative of y = In (tanh x).

A:

Q: find the derivative of y with respect to the appropriatevariable. y = 6 sinh x/3

A: Given function: y=6sinhx3 Using the common differentiation of hyperbolic function: dsinhaxdx=acoshax

Q: at x: つ:8ー5x, atx=e

A: Given:  F(x) = x3 - 5x ...(1)       and the…

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x > 0

A: Given that, y=csc-1x2+1

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (θ + 1) - eθ

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Q: Find the derivative of the function y=cos(3 In x).

A: Given y=cos(3lnx)

Q: Find the derivative of the following function  X=tan(e-y)

A: Given,  X = tane-y    We have to find the derivative of function.

Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

Q: Find the derivative of the function g(x) = (arctan x)³, first showing how to get the formula for -…

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

Q: Find the derivative of the following. y = x2 sin x + 2x cos x - sin x

A: We need to find the derivative of the following, y=x2sinx+2xcosx-sinx

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

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Q: x² sin(x) 8. k(x) = cos( x

A: The given function is kx=x2sinxcosx

Q: 7. y = cos(sin(In(æ))

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Q: Find the derivative of the function. simply if possible y = arccos(e2x)

A: We have to find the derivative of the function: y=cos-1e2x We know the formula of derivatives,…

Q: Find the derivative of the function. Simplify where possible.

A: Here given function gx=1-x2 cos-1x

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: Find the derivative of y with respect to x. y=ln(tan-1(4x5))

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Q: c. Find the derivative of y =+- et x3 cOS X 2

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Q: 3. Find the derivative of the following function. 8(x) = cos"(vx)

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Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

A: