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Standard Formulae - 1

If y = tan(5/...

Question

If y = tan(5/2 pi(t) + pi(6)) then find the value of dy/dt at t=0.

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y = tan (\frac{5}{2} π t + \frac{π}{6})

then find the value of

\frac{d y}{d t}

t = 0

y = x^{3} - 8 x + 7

x = f (t)

\frac{d y}{d t} = 2

x = 3

t = 0

, then the value of

\frac{d x}{d t}

t = 0

Q. Consider the differential equation

\frac{d^{2} y (t)}{d t^{2}} + 2 \frac{d y (t)}{d t} + y (t) = δ (t) w i t h y (t) |_{t = 0} = - 2 a n d \frac{d y}{d t} |_{t = 0} = 0.

. The numerical value of

\frac{d y}{d t} |_{t = 0}

x

y

are differentiable functions of

t

, then show that

\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}}

\frac{d x}{d t} \neq 0

\frac{d^{2} y}{d t^{2}} + y = 0

under the conditions

y = 1, \frac{d y}{d t} = 0

, when t=0 then y is equal to

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