Questions: Directions: In this problem we are going to calculate the derivative of tan(x) using the Quotient Rule. For Steps 1-3, leave your answers in terms of sin x and cos x. Step 1: Write tan(x) in terms of sin(x) and cos(x). tan(x)= Step 2: Calculate the derivative of this expression using the Quotient Rule. Once you differentiate, it may be helpful to remember the trig identity: sin^2(x)+cos^2(x)=1. d/dx[tan(x)]= Step 3: Rewrite your expression from step 2 in the following format. d/dx[tan(x)]=1/cos(x) Step 4: Finally, rewrite this expression in terms of sec(x) and tan(x). d/dx[tan(x)]=

Transcript text: Directions: In this problem we are going to calculate the derivative of $\tan (x)$ using the Quotient Rule. For Steps $1-3$, leave your answers in terms of $\sin x$ and $\cos x$. Step 1: Write $\tan (x)$ in terms of $\sin (x)$ and $\cos (x)$. \[ \tan (x)= \] $\square$ $\square$ $\square$ Step 2: Calculate the derivative of this expression using the Quotient Rule. Once you differentiate, it may be helpful to remember the trig identity: $\sin ^{2}(x)+\cos ^{2}(x)=1$. $\square$ \[ \frac{d}{d x}[\tan (x)]= \] $\square$ $\square$ Step 3: Rewrite your expression from step 2 in the following format. \[ \frac{d}{d x}[\tan (x)]=\frac{1}{\cos (x)} \] $\square$ $\square$ $\square$ Step 4: Finally, rewrite this expression in terms of $\sec (x)$ and $\tan (x)$. \[ \frac{d}{d x}[\tan (x)]=\square \]