Let f (x) =x².cos2(x). what is the correct result of the derivative of f with respect to x? A f (x) = 2xcos(x)[rsin(x)+cos(x)] %3D f'(x) =2xcos(x)[xcos(x) + sin(x В %D © f'(x) =2rcos(x)[sin(x) – xcos(x)] D O f(x)=2rcos(x)[cos(x) – xsin(x)]

Q: f(x) = acos(b\x) x2 COS

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Q: In xy = x² + sin xy

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Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

A: Given query is to find the derivative of the function.

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Q: HiHtar is THe secoyd derivative OF Y

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Q: Find the derivative of the function. rsin(x) y = In(1 + 5v) dv y'(x) = sin x In(1+5 cos x) + cos x…

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Q: Find the derivative of y with respect to x 3tan-1x + sin-1x = 4

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Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt 1 2 arctan(2x) F'(x) = (arctan(Vx)) -

A: Here we have,

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 f(x) = 2(x² + 3x) cos(sin(x³)).

A: I have used product re and derived of composition of two function

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: Find the 46th derivative of y = cos (x) sin (a) cos (2) cos (x) - - sin (x)

A: Given y=cosx

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A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: Evaluate the derivative of y = sin'6x + In /1- 36x, where x= 0.125. dx |x= 0.125 U (Type an integer…

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Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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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.…

Q: Find the derivative of the function.

A: Given: y=lncosxcosx-1

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

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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

Q: The derivative of: y =0( sin (In (0))) in (In (0))) + cos(ln (0)) is is:

A: Given function is rewriting in other variables as: y=x(sin(ln(x)))+cos(ln(x)) Product rule of…

Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

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Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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Q: Use three-point midpoint formula to evaluate the first derivative of y = cos(x) at x =; using a…

A: The three-point midpoint rule to calculate f'(x) is f'(x)≈f(x+h)-f(x-h)2h, where h is the step size.

Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Find the derivative of fcx) = en (sinh Cx)) 5

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Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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Q: What is the second derivative of y = 2x -+ sin x with respect to x? a. 2 -+ cos x b. 2 ++ cos x -+…

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Q: what is the first derivative of cosx^2(x^2+2)

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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: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: Compute forward difference approximations for the first derivative of the function, y = cos(sin(x)+…

A: Given is the function  y=cos(sin(x))+1) Forward difference is found as:F'xi=Fxi+1-FxiΔx

Q: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

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 the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: Find the derivative. 3t cos (t) dt %3D O 3x cos (x4) O &va cos (x4) O 3 cos (x4) - 3x sin (x4) O cos…

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Q: Find the derivative of y with respect to x. y = 4x sin -1 (4x°) + /1– 16x' y = 4x° sin -1 (4x°) +…

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Q: 1. Find the derivative of g(x): Int dt 1+t Cos

A: This will solve by Leibnitz theorem

Q: Find the derivative of y with respect to x.   y= tan-1 *square root (16x2-1) +csc-1*4x ,   x greater…

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

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Q: If e*cos(y) = e" sin(x), show that dy - e*cos(y)-eYcos(x) e*sin(y)+eYsin(x) 3. dx (a) Using the…

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