Find the derivative of y given that y= x In x A None of the given choices 1-In x-x In x B et 1+In x-x In x 1+In x+x In x (D 1-In x+x In x et E.

Q: Find the derivative of y given that y= x In x to ex A None of the given choices 1-In x-x In x B ex…

A: We can find the answer as below.

Q: If the derivative of y = f(x) at x = 2 is equal to " (0 " then y = f(x) is not continuous at r = 2.…

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Q: Let f (x) =e*· cos(x²). what is the correct result of the derivative of fwith respect to x? @…

A: Product rule of differentiation:     Chain rule of differentiation:

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

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

Q: Obtain the derivative of any of the following functions: A) f(x) = 3cotg²3x B) f(x) = 6cos7(3x² – 1)…

A: We use the standard formula of derivatives to solve this problem.

Q: Consider the function below. z²+4 z-2i z # 2i f(z) = (3 + 4i z = 2i Is f(z) continuous at z = 2i? If…

A: Let's solve.

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

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Q: Calculate the derivative d In (t)dt dx 5 using Part 2 of the Fundamental Theorem of Calculus.…

A: Given ddx∫x5e7xlntdt.

Q: Evaluate the derivative of z f8.png asin (bvx3) f(x): %3D c2x + In(kx) if a = 15.08, b = 5, c = 5,…

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Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = In(cos(In 0)) %3D

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Q: 4. Use the definition of derivative to compute the derivative of the following functions at x 1: a.…

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Q: Differentiate. f(x) = In ( In (8x)) f'(x) = Compute the following derivative using the method of…

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Q: Show that the function y=| × | is differentiable on (-o,0) and (O, c0) but has no derivative at x =…

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Q: Find the derivative of f(x) = log, (x° + x – 1). %3D 2 + x - 1 f (2) = %3D (3z* + 1) (In 2) (3z +1)…

A: Given:     fx=log2x3+x-1

Q: Compute the second derivative of  f(x)=ex+x  at x = 2 using a step size h = 0.2  The backward…

A: According to the question; f(x)=ex+x                                                     ; x=2step…

Q: 1. (x*+2x)°(6x²+4)dx 2. [3x²+2x+1 dx 3. (x?)/(x³-4) dx 4. (x+1)/(\x²+2x+1) dx

A: As per the guidelines we can solve 3 problems only.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

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Q: • Estimate the derivative of the following using simple and high- accuracy backward, forward and…

A: (a) fx=1.34x4-3.2x3+0.55x2-1.78 at x=1.2 using h=0.2 and 0.1 estimate the derivative of the…

Q: Find the anti-derivative of g(x) = 2*, which contains the point (0, 2.44). ⒸG(x) = -2 O G(x) = 2 O…

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Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

Q: x In x Find the derivative of y given that y= 1+ In x - x In x A ex 1+ In x + x In x B ex 1- In x+ x…

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Q: Find the derivative of h(z)=(az+b)/q  . Assume that a, b and q are constants. h′(z)=

A: Given function is, h(z)=(az+b)q where a, b & q are constants.

Q: Which of the following represents the derivative of y=cos x at x=n? cos(1 – h) lim h-0 h cos(h) –…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: Suppose F(z) = | e dt. Use the Fundamental Theorem of Calculus to evaluate the derivative. 13 F'(포)…

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Q: Let y = f(x) be an positive increasing function defined for x > 0. The length of the curve described…

A: Given:         Length of curve y=f(x) is between x=0 and x=t is equal to14t4+t2+lnt+4+t2−ln2.

Q: Find 20 and by implicit differentiation, and confirm that the results obtained agree with those…

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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Q: 3. Find the derivative of ywith respect to x in the following functions: 18x y (3x-2 + 4x) x'- 3 a)…

A: Please see the explanation below

Q: Let f (x) =e*. sin(x²). what is the correct result of the derivative of f with respect to x?…

A: This question is related to differentiation, We will solve it using given information.

Q: (2) The derivative of r at the попzеrо real nuтвer a is Dr.(h) = -h/a². Proof. (1) Compute, p(a + h,…

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Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: Consider the function f(x) = 3cos(2x). (a) Find the derivative of f(x). (b) Verify that the…

A: (a) Given function is f(x)=3cos(2x) The derivative, f'(x)=-6sin(2x)

Q: Assuming that x> 0, use differentiation to justify the formula X dx = In |x| + C. (=| d dx = In |x|+…

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Q: suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A: According to quotient rule of differentiation, ddxuv=vdudx-udvdxv2 The value of ddxuv at x=1 will…

Q: The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x…

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

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Q: If f(x) = x[5 sin (In x) + 2 cos (In x)], find the first derivative f'(x). A. x[3 sin (In x) + 7 cos…

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Q: Find the derivative of the function. h(t) = Part 1 of 5 Apply the general power rule which states…

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Q: ind the derivative of y with respect to x. y =-cos-16x + 7° 6 6. 1 + (6x + 7)2 81 - (6x + 7)2 O 4.…

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Q: 5. Compute the derivative, r'(t), of r(t) = (et-4, t, In(1 – t)).

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Q: 4. Find the second-order derivative of the following function: f(z) = log, cos z + In %3D

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Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

Q: Show that the following function is continuous at x = 1 for all values of p. (px + 1, if x > 1 f (x)…

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Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: Let f (x) = x sin x and g(x) = x cos x. (a) Show that f ,(x) = g(x) + sin x and g ,(x) = −f (x) +…

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