Fichas
C3 Differentiation
Fichas del conjunto (22)
- 1y = lnxdy/dx = 1/x (no more ln)
- 2y = e^xdy/dx = e^x (no change)
- 3y = e^(ax+b)dy/dx = ae^(ax+b) (differentiate power)
- 4y = ln(ax+b)dy/dx = a/(ax+b) (differentiate and put over original bracket) (no more ln)
- 5what is the gradient?dy/dx
- 6what is a stationary point?when dy/dx (gradient) = 0
- 7nature of stationary point?when d^(2)y/dx^(2) is bigger/smaller than 0
- 8minimum is when..?bigger than 0
- 9maximum is when..?smaller than 0
- 10what is the equation of a line?y-y1 = m(x-x1)
- 11what is the equation of the normal?same -> y-y1=m(x-x1) but m is the negative reciprocal of the gradient of the tangent (which is dy/dx)
- 12if it asks for only integers in the equation of the line..?make sure there is only whole numbers - no fractions!
- 13The chain rule?if f(x) = (ax+b)^(n) then
dy/dx = n . f^1(x) . f(x)^(n-1) - 14the product rule?if y = u . v then
dy/dx = V.du/dx + U.dv/dx - 15to fully simplify...sometimes can take out a common factor and put in brackets!
- 16to differentiate completely...sometimes you have to do more than one product rule, or combine with chain rule, quotient etc
- 17the quotient rule?if y = u/v then
dy/dx = (V.du/dx - U.dv/dx)/ V^2 - 18remember...- may combine quotient, product, chain rule
- usually don't expand bracket on bottom - 19dx/dy?1/(dy/dx) = reciprocal of dy/dx =
reciprocal of gradient - 20rates of change? e.g. N = e^(1.5t) when t = 6differentiating with respect to time (so dy/dt)
so dN/dt = 1.5xe^(1.5t)
when t=6 -> 1.5xe^(1.5x6) -> 12155 years - 21if they ask with a SHAPE? e.g. circular puddle, radius increasing at rate of 3cm per minute, what is rate of change of area when radius is 15cm?dr/dt = 3 <- GIVEN IN Q
we need to find dA/dt
dA/dt = (dr/dt) x (dA/dr) <- CHAIN RULE
so need to find dA/dr to use ^
find an equation of shape that has A and r
A = (pi)r^2
so now we can find dA/dr
dA/dr = 2(pi)r
so dA/dt = 3 x 2(pi)r
when r=15 -> 3 x 30(pi)
ANSWER = 90(pi) - 22if equation of shape gives you dr/dA and you need dA/dr?use the rule that dx/dy = reciprocal of dy/dx
Información
- Descripción
- A level (C3) Maths Fichas sobre C3 Differentiation, creado por Maisie Carroll el 25/02/2017.
- Creado por
- Maisie Carroll
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