Let f be a differentiable function. If h (x) = (2 +f (sin x)) ',which of the following gives a correct process for finding h (x) ?

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Consider the function f(x) whose second derivative is f''(x) = 3x +4 sin(a %3D If f(0) = 3 and f'(0)…

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Q: Consider the function f(x) whose second derivative is f''(x) = 8x + 6 sin(x). If f(0) = 2 and f'(0)…

A: Given  f''(x) = 8x+6 sin(x),  f(0)=2,  f'(0)=4 We have to find the value of f(3).

Q: The derivative with respect to X .2 y = x sin-'x + V1 – x²

A: Given:               y=x sin-1x+1-x2 Differentiate with respect to x           ddxy=ddxx sin-1x+1-x2…

Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Assume that y = sin'x is a differentiable function of x. By differentiating the equation x= sin y…

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Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Assuming that z is a differentiable function of x and y, use implicit differentiation to find from…

A: ln(x2y) - eyz= tan-1z  ----(1)To Find: ∂z∂ySince z is a function of x and ySo we differentiate…

Q: Consider the function f (x) = sin β x,where β is a constant.   Verify that the function and its…

A: A function of the form p(q(x)) has its derivative by chain rule equal to p'(q(x))q'(x). For the…

Q: The derivative of the function y = sin-1(e* – In x), where Je – In x| < 1, is:

A: Recall ddx(sin-1(x))=11-x2 ddx(ex)=ex ddx(ln(x))=1x

Q: . Find the derivative with respect to x: y = tan¬(Vx² –- 1) + csc¯²(x),x > 1

A: Given thaty=arctanx2-1+arccscx To find its derivative

Q: Use the First Derivative Test to find the relative extrema of ƒ(x)=· sin x on (0,27).

A: The given function is- fx=x2-sinx  Differentiating f(x) w.r.t x- f'x=12-cosx Put f'x=0,…

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: Əz Assuming that is a differentiable function of and y, use implicit differentiation to find from t…

A: Implicit differentiation

Q: Consider the function f(x) whose second derivative is f′′(x) = 18x + 3 cos x. If f(0) = 4 and f′(0)…

A:

Q: Consider the function f(x) whose second derivative is f''(x) 8x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given : f"(x) = 8x + 3 sinx, f(0) = 4, f'(0) = 4,    To find : f(5)?

Q: Use the definition of a derivative to find f'(0) where: x² sin () lo x + 0 f(x) If the derivative…

A: follow next step

Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

A:

Q: Assume that y = sin-1x is a differentiable function of x. By differentiating the equation x = sin y…

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

A:

Q: Assume that y = sin-1 x is a differentiable function of x. By differentiating the equation x = sin y…

A: The given equation is

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 4 sin(x). If f(0) = 2 and f'(0)…

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Q: Suppose that y is a differentiable function of x and w = sin(y2). Express the derivative of w with…

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Q: Consider the function f (x) whose second derivative is f"(x) = 10x + 8 sin(x). If f (0) = 2 and…

A: Given function is

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

A:

Q: Find a positive value, c, for x, thot satisfies the Mean valve Theorem for derivatives for…

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Q: b) Use the definition of the derivative to compute f'(x) for 1)f(x) = 2v-5x + 9, 2)f(x) = x sin 3x…

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Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

A:

Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 6 sin(x). If f(0) = 2 and f'(0) =…

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…

A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…

Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…

A: Given: (1) f(x) = sin x / x  at x = π/6  (2).  f(x) = ex sinx at  x= 0 (3).  f(x) =  cos x / ex   at…

Q: Compute for y" by implicit differentiation. sin y + cos x 1

A: This question is based on diffrentiation of implicit function.

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: Consider the function f(x) whose second derivative is f''(x) = 5x + 7 sin(x). If f(0) = 2 and f'(0)…

A: Given :f''(x)=5x+7sin(x)

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

A:

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinaxdx=-cos(ax)a+c ∫cosax dx=sin(ax)a+c ; where 'c' is an integration…

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 7 sin(x). If f(0) = 2 and f'(0)…

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

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Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)

A: Find the derivative of function

Q: Use the definition of a derivative to find f' (0) where: x² sin() x + 0 f(x) = x = 0 If the…

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Q: Find the values of x on [0, 2 ) π where the tangent line of f x( ) be horizontal. y=e^-x (cosx)

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Q: Find the derivative off with respect to x of f(x) = In x⁹. The derivative off with respect to x of…

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Q: For which  x value(s) is the function  f ( x ) = sin ^− 1 ⁡ ( 2 x )  defined and not differentiable?

A: Given that the function is       f(x) = sin-1(2x)  Here we have to find those values of x, in which…

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: Consider the function f(x) whose second derivative is f''(x) = 7x + 7 sin(x). If f(0) = 2 and f'(0)…

A: We need to find f(5).