QCEVault

Differentiation of trigonometric functions and differentiation rules — Question 280

Original QCE Vault practice · 4 marks

Q280 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 280 (4 marks)

Let f(x)=excos⁡xf(x)=e^x\cos x.
a)
Determine f′(x)f^{\prime}(x).
[1 mark]
b)
Determine f′′(x)f^{\prime\prime}(x) in simplified form.
[2 marks]
c)
State whether the curve is concave up or concave down at x=π6x=\dfrac\pi6, with justification.
[1 mark]
Question linkSyllabus coverage

Related questions

  1. Q2 · Original practice · 1 mark
    Determine ddx[tan⁡(3x)]\dfrac{d}{dx}[\tan(3x)].
    Differentiation of trigonometric functions and differentiation rules
  2. Q12 · Original practice · 1 mark
    If h(x)=x2sin⁡xh(x)=x^2\sin x, then h′(x)h'(x) is
    Differentiation of trigonometric functions and differentiation rules
  3. Q22 · Original practice · 1 mark
    For f(x)=sin⁡x1+cos⁡xf(x)=\dfrac{\sin x}{1+\cos x}, where defined, f′(x)f'(x) simplifies to
    Differentiation of trigonometric functions and differentiation rules
  4. Q27 · Original practice · 2 marks
    Differentiate y=2sin⁡x+cos⁡(2x)y=2\sin x+\cos(2x).
    Differentiation of trigonometric functions and differentiation rules