Find the Derivative of the given function. If f(t) = tan '(In(t")) . then f'(t) If g(t) = In(tan (2t)), then d(t) 0

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= ln x3

A: Given:

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

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 the derivative of y with respect to x, t, orθ, as appropriate.

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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  y=sin^-1(cos(x))

A: We can find the derivative as below

Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, 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 x of y = xlnx – x.

A: Using rules of differentiation.

Q: find the derivative of y with respect to the appropriatevariable. y = x sin-1 x + √(1 - x2)

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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 y with respect to the appropriatevariable. = sin-1 (1 - t)

A: Given Trigonometric Expression: sin-11-t We can differentiate this trigonometric function with the…

Q: Find the derivative of function.

A:

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

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

Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: Find the derivative with respect to x: y = tan(Vx2 – 1) + csc-(x),x > 1

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (3te-t)

A: We expand the function using the properties of logarithm

Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

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: 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

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

A: The given function is y=1+ln t1-ln t

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 z=(ln5)e^x dz/dx=

A:

Q: find the derivative of y with respect to x, t, orθ, as appropriate.

A: On simplification, we get

Q: Find the derivative of  y=ln [tan-1(7x5)] with respect to x.

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = x4/4 ln x - x4/16

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Q: find the derivative of y with respect to the appropriatevariable. y = (x2 + 1) sech (ln x)

A: Given: y=x2+1sechlnx

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln (t3/2) + √t

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Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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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 y with respect to x, t, or θ, as appropriate. y = ln (sin x)

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Q: Give the derivative of f(x) arctan an(e³*) at the point where x = 0.

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (2e-tsin t)

A: On simplification, we get

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1/ln 3x

A: Given:

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: Find the derivative of the function.   y = In(x)/x9

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Q: Find the derivative of h(x) = (1+ cos x)*

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

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Q: Find the derivative of y with respect to x. y = 3 sin -1 (5x 3)

A: Given data:     The given expression is: y=3sin-1(5x3).   Assume 5x3=u and differentiate it with…

Q: Find the derivative of y with respect to x    y=ln(x-7)

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Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (cos2 θ)

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

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

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Q: find the derivative of y with respect to the givenindependent variable. y = 2x

A: y=2x

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

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Q: Find the derivative of y = arccos x + x 1-x²

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Q: Find the first derivative of v with respect to x

A: Given,

Q: find the derivative of y with respect to the givenindependent variable. y = 3-x

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