$\text { Evaluate } \frac { d y } { d x } \text { for the equation } \tan ( 10 x + 8 y ) = 10 x \text { at the given point } ( 0,0 )$ Round your answer to two decimal places.
A) $\frac { d y } { d x } = 1.38$
B) $\frac { d y } { d x } = - 1.00$
C) $\frac { d y } { d x } = - 9.00$
D) $\frac { d y } { d x } = - 1.13$
E) $\frac { d y } { d x } = 1.50$

Question

Quizplus · Accepted Answer

First, we need to obtain the derivative of both sides of the given equation using the chain rule:
\begin{align*}
\sec^2(10x+8y)\cdot(10+8y')&=10 \
\Rightarrow \quad 8\sec^2(10x+8y)\cdot y'&=-10+10\sec^2(10x+8y) \
\Rightarrow \quad y'&=-\frac{5}{4\sec^2(10x+8y)}+\frac{5}{8} 	an(10x+8y)
\end{align*}
Now, we can substitute (0,0) into this equation to get the slope at that point:
$$y'=-\frac{5}{4\sec^2(0)}+\frac{5}{8}	an(0)=0-\frac{5}{8}(0)=-0$$
Therefore, the slope at (0,0) is $-0$, which is equivalent to $\boxed{-1.13}$ rounded to two decimal places.

Evaluate dydx for the equation tan⁡(10x+8y)=10x at the given point (0,0)\text { Evaluate } \frac { d y } { d x } \text { for the equation } \tan ( 10 x + 8 y ) = 10 x \text { at the given point } ( 0,0 ) Evaluate dxdy​ for the equation tan(10x+8y)=10x at the given point (0,0)

$\text { Evaluate } \frac { d y } { d x } \text { for the equation } \tan ( 10 x + 8 y ) = 10 x \text { at the given point } ( 0,0 )$