Find the slope of the tangent line to the curve at the given point. (Calculus II)

Question

anonymous · Answer

No, this is Calculus I, I'm pretty sure.

agent_a · Answer

HOLD ON I AM STILL POSTING THE PHOTO. SMART ALLECKS.

agent_a · Answer

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anonymous · Answer

The slope of the tangent line to $f(x)$ at point $(x_0,y_0) $ is $f'(x_0)$.

anonymous · Answer

Okay, in this case  $y=f(x)$ I presume, and so $f'(x) = dy/dx$.

anonymous · Answer

$$
\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}
$$

agent_a · Answer

And just as a note, the $$\frac{ dy }{ dx } = \frac{ 4 }{ 9 }$$ is the answer to the problem.

anonymous · Answer

$$
\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} =\frac{y'(t)}{x'(t)}
$$

agent_a · Answer

Got it. Perfect. Thanks!

anonymous · Answer

Remember that: $$
\frac{dy}{dt} = \frac{dy}{dx}\frac{dx}{dt}
$$We just use chain rule and solve for $dy/dx$.