For `f(x) = log_e (x^2 + 1)`, find `f prime (2)`. (2 marks)
Calculus, MET1 2009 ADV 2b
Let `y=ln(3x^3 + 2)`.
Find `dy/dx`. (2 marks)
Calculus, MET1-NHT 2018 VCAA 1b
Let `y= (x + 5) log_e (x)`.
Find `(dy)/(dx)` when `x = 5`. (2 marks)
Calculus, MET1 2015 VCAA 1b
Let `f(x) = (log_e(x))/(x^2)`.
- Find `f′(x)`. (2 marks)
- Evaluate `f′(1)`. (1 mark)
Calculus, MET1 2012 ADV 12ai
Differentiate with respect to `x`
`(x - 1)log_e x` (2 marks)
Calculus, MET1 2008 ADV 2aii
Differentiate with respect to `x`:
`x^2log_ex` (2 marks)
Calculus, MET2 2011 VCAA 4 MC
The derivative of `log_e(2f(x))` with respect to `x` is
- `(f′(x))/(f(x))`
- `2(f′(x))/(f(x))`
- `(f′(x))/(2f(x))`
- `log_e(2f′(x))`
- `2log_e(2f′(x))`
Calculus, MET1 2007 VCAA 2b
Let `g(x) = log_e(tan(x))`. Evaluate `g′(pi/4)`. (2 marks)
Calculus, MET1 2009 VCAA 1a
Differentiate `x log_e (x)` with respect to `x.` (2 marks)
Calculus, MET1 2013 VCAA 1a
If `y = x^2 log_e (x)`, find `(dy)/(dx)`. (2 marks)