What is the gradient of the function f(x) = 5 sin(5x) A sin(5x) - sin(5x) E B 25 cos(5x) F -cos(5x) 25 sin(5x) G -5 sin(5x) - 25 cos(5x) H. cos(5x)

Q: Does the function cos x х f(x) = 0, x = 0 have a derivative at x = 0? Explain.

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Q: Step 3 Now write the derivative in terms of x by recalling that u = -3x + 7 and v = x + 7. du 1 +=…

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Q: Find the derivative of f(w)= sin(4w²)+cos(4w²). A) Swcos(4w°)–8wsin(4w²) B) -8wcos(4w?)+8wsin(4w²)…

A: Given function is  f(w)=sin(4w2)+cos(4w2)Derivative of f with respect to w:f'(w)=…

Q: What is the derivative of x 3 sin(x)? Select one: (sin(x) + 3x cos(x)) 2 Зх 3 + cos(x) 2 Зх 3 2 O…

A: Derivative of the function

Q: Calculate the derivative using implicit differentiation: சம dz || -2zw - 7y (x³ +8w+z²) θω dz…

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Q: sin(x) + cos(y) 1 + sin(x) cos(y).

A: Given query is to find the dy/dx at x = 0 and y = π/2

Q: sin(x') In(5x + 7x- 3) 6) Find the derivative of: y =

A: Formula 1: Let f(x) and g(x) be two functions, then f(x)g(x)=g(x)f'(x)-f(x)g'(x)(g(x))2 The given…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

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Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = cos(x) at x =…

A: Given function is y=cosx. We have to evaluate the first derivative of y=cosx at x=π4 using a value…

Q: hCt)-5t (1-ビ ((チ1) (け)

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

Q: Apply the Second-Derivative Test to find all relative extrema of the function  f(x)=cosx-x ,…

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