### Home > APCALC > Chapter 11 > Lesson 11.4.1 > Problem11-107

11-107.

Write the derivative, $\frac { d y } { d x }$, of each equation below.

1. $x \sin(y) - 10y^2 = y \ln(x)$

$\sin(y)+x\cos(y)y^\prime-20yy^\prime=y^\prime\ln(x)+\frac{y}{x}$

1. $r = 2 - \cos(θ)$

$\frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

$x=r\cos(\theta)=(2-\cos(\theta))\cos(\theta)$

1. $\left\{ \begin{array} { l } { x ( t ) = 4 t - t ^ { 2 } } \\ { y ( t ) = \operatorname { cos } ( 2 t ) } \end{array} \right.$

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

1. $y = x \sec\sqrt { 2 x ^ { 3 } - 4 x }$

$\text{Let }w=\sqrt{2x^3-4x}.$

$y^\prime=\sec(w)+x\sec(w)\tan(w)w^\prime$

What is $w′$ ? Substitute $w$ and $w′$  into the equation in Step 2.