### Home > APCALC > Chapter 6 > Lesson 6.2.2 > Problem6-78

6-78.

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

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

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

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

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

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

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

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.

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

Use implicit differentiation.

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