What is the derivative of $f (t) = (ln t, - 3 t^{3} + 5 t)$ $f(t) = (lnt, -3t^3+5t )$ ?

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What is the derivative of $f (t) = (ln t, - 3 t^{3} + 5 t)$ $f(t) = (lnt, -3t^3+5t )$ ?

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Answer 1 · 2018-07-17T15:03:59

$\frac{d y}{d x} = - 9 t^{3} + 5 t$ $dy/dx=-9t^3+5t$

Explanation:

We have

$x (t) = ln (t)$ $x(t)=ln(t)$

$y (t) = - 3 t^{3} + 5 t$ $y(t)=-3t^3+5t$
given.So we get

$\frac{d x}{d t} = \frac{1}{t}$ $dx/dt=1/t$

$\frac{d y}{d t} = - 9 t^{2} + 5$ $dy/dt=-9t^2+5$

then

$\frac{d y}{d x} = \frac{\frac{d y}{d t}}{\frac{d x}{d t}} = \frac{- 9 t^{2} + 5}{\frac{1}{t}} = - 9 t^{3} + 5 t$ $dy/dx=(dy/dt)/(dx/dt)=(-9t^2+5)/(1/t)=-9t^3+5t$

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What is the derivative of $f (t) = (ln t, - 3 t^{3} + 5 t)$ $f(t) = (lnt, -3t^3+5t )$ ?

1 Answer

Explanation:

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What is the derivative of f(t) = (lnt, -3t^3+5t ) f(t)=(lnt,−3t3+5t)f(t) = (lnt, -3t^3+5t ) ?

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Explanation:

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What is the derivative of $f (t) = (ln t, - 3 t^{3} + 5 t)$ $f(t) = (lnt, -3t^3+5t )$ ?