CPM Homework Help : CALC Problem 6-78

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Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem 6-78

6-78.

For each of the following functions, find $\frac { d y } { d x }$ .

$y = 3 ^ { e ^ { 3 x } }$
Hint (a):
Use the Chain Rule. You may have to use it more than once.
Nore Help (a):
The derivative of $a^x$ is $(\operatorname{ln a)} · a^x$ . For $e^x$ , due to the nature of $\operatorname{ln}$ , its derivative is itself.

$x ^ { 2 } \frac { d y } { d x } - 3 y = 2 \frac { d y } { d x }$
Hint (b):
$y'=\frac{4+y\text{sin}x}{\text{cos}x}$

$y = \int _ { 2 } ^ { x } ( \operatorname { ln } (t ^ { 2 }) - 4 ) d t$
Hint (c):
What is the derivative of an integral?
Also, should your result be in terms of $t$ or in terms of $x$ ?
To answer this, imagine the result of actually integrating the function first before differentiating it.

$y \operatorname { cos }( x )- 4 x = 8$
Hint (d):
Use implicit differentiation.

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