Show that J (x) = 2 sin x

Q: Find a result by using undetermined coefficients for ý + y = x² + x+sin(2x)

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Q: Find the general solution of f′(x) = −2x sin x2 .

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Q: Determine f sin x sin(cos x) dx

A: We have to solve the problem

Q: Differentiate (a) y − sin(x2) and (b) y − sin2x.

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Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: Where are the functions f1(x) = ∣sin x∣ and f2(x) = sin ∣x∣ differentiable?

A: We graph f1(x) = ∣sin x∣  using a graphing calculator. We see that, at x=nπ, there are cusps.…

Q: Find f) sin cx) F(X): 1t cos (x)

A: Find two times derivative at given value

Q: Differentiate the function. g(x)  =x Sin(2x)

A: We will use the product rule

Q: Differentiate the function   f(x) =    sin x  ln ( 5x )

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Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: Find f'(x) if ƒ (x) = 6 cos x + 10 sin x. S'(x) =|

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Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Find if, y - x = sin(xy)

A: In this question we will use differentiation property for solving this question and after that we…

Q: Find the definite integral.

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Q: (В) f (x) 3 3 sin(2x) — 4

A: we have to draw the curve of the function fx=3sin2x-4 let y=f(x). therefore, y=fxy=3sin2x-4 the…

Q: 6. Differentiate. a) f(x) = In (sin²x) b) g(x) = In (xe-2*)

A: Write sin2x as (sinx)2 and simplify the terms and use the log property to simplify the term and…

Q: Differentiate the function y=sin^2 x

A: Given: y=sin2(x)

Q: Find f' (x), if f(x) = sin(2x* – sin(x))

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Q: Consider the function f(x) whose second derivative is f''(x) = 2x + 2 sin(x). If f(0) = 3 and f'(0)…

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Q: Find F(x), f"(x) and f''(x) for f(x)=13x2+ sin(15x).

A: Given,            fx=13x2+sin15x

Q: Evaluate (a) 2. Sinx+ X=X (1) Sinx dx T+x²

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Q: Evaluate the integral. sin(5.x) sin(4x) dx

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Q: 2. Differentiate. f(t) = et sin(2t)

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Q: If f(x) = 7 sin(8a)sin-(x), f'(x) -

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Q: Find a function F(x) satisfying F'(x) = sin(6x).

A: Solution  Let consider differential  F'(x)  of function F(x)  so F(x)=∫F'(x)…

Q: Compute / sin x •cos1º x dx.

A:

Q: 2. Differentiate each function with respect to x: (a) y = cos (3x²) (b) y = sin (1 + 3x)

A: Our Aim is to differentiate the given functions with respect to x:-(a) y=cos (3x2)(b) y= sin (1+3x)

Q: Differentiate the function. f(x) = sin(7 In(x)) %3D f'(x) =

A: Given function :

Q: Find f'(x) where f(x) sin(cos(4x2 +1))

A: Consider the given function

Q: Evaluate f sin (2(V1-) dx

A:

Q: Consider the function f(x) whose second derivative is f"(x) = 7x + 10 sin(x). If f(0) f(x)? 3 and…

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: Use the second fundamental theorem calculus along with the chain rule to find sint dt dx sinx 2x…

A: We have to find          ddx∫1xsint dt using the second fundamental theorem calculus along with the…

Q: 2. Use the Intermediate Value Theorem to show that the equation sinx = x – 1 has at least one real…

A: In the question it is asked to calculate real solution of equation sinx = x-1. Also, it is asked to…

Q: Consider the function f(x) whose second derivative is f"(x) = 10x + 10 sin(x). If f(0) = 4 and f'(0)…

A: Given that: f''(x)=10x+10sinx

Q: Find f'(x) where f(x) = x*in(#) + (sin(x))".

A: Given that, fx=xsinx+sinxx To find the derivative of this fx=xsinx+sinxx, take the logarithmic on…

Q: Differentiate the function. f(x) = 5 sin2(x) − 8 cos2(x)

A: Given:

Q: differentiate the function  y=(x^4 sin^2(x))^(3x)

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Q: differentiate the function: y= ln(x^9 sin^2(x)) y'(x)=

A: Given function as

Q: Differentiate the function. f(x) = sin(x) In(3x) f '(x)

A: Here, you can use the product rule for derivative. ddx(u·v)=u·v'+v·u'

Q: Find a fixed point of x=g(x)=}+}sin(3x). ||

A: Given that                      x=g(x)=12+14sin3x To find a fixed point of the above equation we…

Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: Hi, I need help with this step-by-step please.

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Q: Determine 2 x sin x dx

A: We can find the integration as multiplication of two functions and then using ILATE rule to…

Q: f(x) = x in the %3D sin 2x + ...

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Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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Q: Differentiate the function. y= (Sin x)In x

A: Given function - y = sinxlnx                   .............(1)Taking logarithm ln on both sides -…