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A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .
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A: First, we simplify the given function using the multiplication and power rule of logarithm.
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Q: How do I verify d/dx(cos^-1(x))=-1/(sqrt(1-x^2)) using implicite differentiation?
A: Verify the result by implicit differentiation as follows.
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A: Given y=sin(2x)cos2x The product rule of derivative is given by:
Q: Which is the derivative of y= sin (x2-2x + 1)? (2х -2) (2x-2)Cos(x²-2x + 1)
A: We have to find derivative
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Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T
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A: Derivative of the function is given below
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Q: Find the derivative of the function. f(x) = sin-(4x) f'(x) = %3D
A: The given function is: f(x)=sin-1(4x) To find f'(x) here.
Q: Find the derivative of the function.
A: The given function is y=ln5sinx
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Q: compute the derivative. y = sin(2x) cos2 x
A: We can find the derivative of this function by using the product rule of differentiation . According…
Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…
A: Given that: Let f(x)=cos(1-x)
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A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)
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Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…
A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…
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Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].
A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].
Q: g(x) = cos ¹x+ 1-x
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Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1
A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…
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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: sinx In (2) co cos x
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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+V3 2V3 At the…
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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…
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Q: find the derivative of sin (ax + b) cos (cx + d) CX
A: According to product rule of differentiation ,and according to chain rule of differentiation ,.
Q: Find the derivative of y = 2x cos x − 2 sin x.
A: Given function y=2xcosx-2sinx dydx=ddx2xcosx-2sinx=ddx2xcosx-ddx2sinx Recall the formula…
Q: 1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x
A: we are given the function is f(x)=1+sin2x2cos3x
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Q: Find the derivative of y=x?sinx x?cosx +2xsin x 2xcos x x2 sin x+2xcos x x2cosx
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Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to
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Q: Find the derivative of f(x) = 2x(sinx)cos(x) ? a. f(x)=sin2x+2xcos2x b. f(x)=2sin2x+2xcos2x c.…
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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: limit x to 0 3x-3xcox/sin^2(3x)
A: Here given limit as Use the L'hospital rule which states
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: 3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x
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Q: What is the derivative of the: y = (1 + cos2 x sin x2)3/2
A: Given: y=1+cos2x sinx232 differentiate with respect to x, dydx=ddx1+cos2x sinx232dydx=321+cos2x…
Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…
A: Given:- y = (-7x2-5x+5) (sin(x) +11x) To find:- Derivative of y
Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)
A: Find the derivative of function
Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.
A: Sum/difference rule of differentiation,
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Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2
A: We have to find out derivative
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