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Home > APCALC > Chapter 9 > Lesson 9.4.2 > Problem 9-122

9-122.

For each of the following equations, what is $\frac { d y } { d x }$ ?

$y \ln(x) = x^2$
Step (a):
$y^\prime\ln(x)+\frac{y}{x}=2x$
Hint:
Now solve for $y^\prime$ .
More Help:
$y=\frac{x^2}{\ln(x)}$

$\frac { d ^ { 2 } y } { d x ^ { 2 } }= 3x^2 − 2x$
Hint (b):
$\int\frac{d^2y}{dx^2}=\frac{dy}{dx}+C$

$( \frac { x } { 2 } ) ^ { 2 } + ( \frac { y } { 3 } ) ^ { 2 }= 1$
Step (c):
$2\Big(\frac{x}{2}\Big)\Big(\frac{1}{2}\Big)+2\Big(\frac{y}{3}\Big)\Big(\frac{1}{3}\Big)\Big(\frac{dy}{dx}\Big)=0$

$y =| 2 x |$
Hint (d):
Graph this function. How can you describe the slope of the curve?

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