Differentation Flashcards
sin(kx)
kcos(kx)
cos(kx)
-ksin(kx)
e^kx
ke^kx
ln(x)
1/x
What is the chain rule for (2x-1)^2 ?
2(2x-1)x(2)
What is the chain rule for (sin2x+4x)^3 ?
3(sin2x+4x)^2)x(2cos2x +4)
What is the product rule ?
uv’ x vu’
What is the quotient rule for u/v ?
vu’ - uv’ / v^2
tan(kx)
ksec^2(kx)
cosec(kx)
-kcosec(kx) cot(kx)
cot(x)
-kcosec^2 (kx)
sec (kx)
ksec(kx) tan(kx)
What is the method for differentiating parametric equations?
dy/dt / dx/dt
What is the method for implicit differentiation?
Differentiate x and every time you differentiate y x dy/dx
How do you know if a curve is concave?
f’‘(x) less than or equal to 0
How do you know if a curve is convex?
f’‘(x) more than or equal to 0
How do you differentiate from first principles?
lim h->0
f(x+h) - f(x) / h
How do you know if a curve is decreasing?
f’(x) is less than or equal to 0
How do you know if a curve is increasing?
f’(x) is more than or equal to 0
How do you know if a stationary point is a maximum?
f’‘(x) is less than 0
How do you know if a stationary point is a minimum?
f’‘(x) is more than 0
What if at a stationary point has f’‘(x) = 0 ?
Check again using f’(x) and two values on either side of the point
