Question

please check my answer!

Answer 1

okay so x = t + 6 and y = t^2+10t

Answer 2

first derivative is dy/dx = 2t+10/1

Answer 3

second derivative d^2y/dx^2 = 2/1

Answer 4

please check my answers

Answer 5

What do you want to do?

Answer 6

i just want you to check my answer

Answer 7

@perl could you come check my answer real quick

Answer 8

$$
\Large{
x = t + 6\\ y = t^2+10t
\\
\frac{dy}{dx} =\frac{\frac{dy}{dt}}{\frac{dx}{dt}}= \frac{2t+10}{1} =2t+10\\
\\ \therefore \\
~~~~~\frac{d^2y}{dx^2}\\ = \frac{d}{dx} \left( \frac{dy}{dx} \right)\\
= \frac{d}{dx} \left( 2t+10 \right)\\= \frac{d}{dt} \left( 2t+10 \right)\cdot \frac{dt}{dx}\\
=\frac{\frac{d}{dt} \left( 2t+10 \right)}{\frac{dx}{dt}}\\
= \frac{2}{1}= 2
}
$$

Answer 9

note that I used the chain rule
$$
\Large{

\frac{df}{dx}= \frac{df}{dt} \cdot \frac{dt}{dx}
}
$$

Answer 10

because
$$
\Large{

\frac{df}{dt} \cdot \frac{dt}{dx}

=\frac{df}{{\cancel {dt}}} \cdot \frac{\cancel {dt}}{dx}=\frac{df}{dx}
}

$$