CPM Homework Help : APCALC Problem 6-78

For each of the following equations, write an equation for $\frac { d y } { d x }$ .

$y = 3^{e^{3x}}$

Hint (a):

Use the Chain Rule. You may have to use it more than once.

Hint (a):

The derivative of $a^x$ is $(\ln a) · a^x$ . For $e^x$ , due to the nature of $\ln$ , its derivative is itself.

$x^2\frac { d y } { d x }− 3 y = 2\frac { d y } { d x }$

Hint (b):

$\text{Use algebra to solve for }\frac{dy}{dx}.$

$\int _ { 2 } ^ { x } ( \operatorname { ln } ( t ^ { 2 } ) - 4 ) d t$

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.

$y \cos(x) - 4x = 8$

Hint (d):

Use implicit differentiation.

Answer (d):

$y'=\frac{4+y\text{sin}x}{\text{cos}x}$